X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=weblib%2Farithmetics%2Fnat.ma;h=a592b1377dfc9815c0d4f706193bab46e1218a4f;hb=8095279ddfb0e36b417115f94c60622caf4bfdab;hp=2260506329463e418b25706942c942bd3cf1c481;hpb=98827f140349f91cbd546491b233d6d5d3f335c3;p=helm.git

diff --git a/weblib/arithmetics/nat.ma b/weblib/arithmetics/nat.ma
index 226050632..a592b1377 100644
--- a/weblib/arithmetics/nat.ma
+++ b/weblib/arithmetics/nat.ma
@@ -687,14 +687,14 @@ theorem monotonic_lt_times_r:
   ∀c:a href="cic:/matita/arithmetics/nat/nat.ind(1,0,0)"nat/a. a href="cic:/matita/arithmetics/nat/nat.con(0,1,0)"O/a a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a c → a href="cic:/matita/basics/relations/monotonic.def(1)"monotonic/a a href="cic:/matita/arithmetics/nat/nat.ind(1,0,0)"nat/a a href="cic:/matita/arithmetics/nat/lt.def(1)"lt/a (λt.(ca title="natural times" href="cic:/fakeuri.def(1)"*/at)).
 #c #posc #n #m #ltnm
 (elim ltnm) normalize
-  [/span class="autotactic"2span class="autotrace" trace a href="cic:/matita/arithmetics/nat/monotonic_lt_plus_l.def(9)"monotonic_lt_plus_l/a/span/span/ 
+  [/span class="autotactic"2span class="autotrace" trace a href="cic:/matita/arithmetics/nat/monotonic_lt_plus_l.def(5)"monotonic_lt_plus_l/a/span/span/
   |#a #_ #lt1 @(a href="cic:/matita/arithmetics/nat/transitive_le.def(3)"transitive_le/a … lt1) //
   ]
 qed.
 
 theorem monotonic_lt_times_l: 
   ∀c:a href="cic:/matita/arithmetics/nat/nat.ind(1,0,0)"nat/a. a href="cic:/matita/arithmetics/nat/nat.con(0,1,0)"O/a a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a c → a href="cic:/matita/basics/relations/monotonic.def(1)"monotonic/a a href="cic:/matita/arithmetics/nat/nat.ind(1,0,0)"nat/a a href="cic:/matita/arithmetics/nat/lt.def(1)"lt/a (λt.(ta title="natural times" href="cic:/fakeuri.def(1)"*/ac)).
-/span class="autotactic"2span class="autotrace" trace a href="cic:/matita/arithmetics/nat/monotonic_lt_times_r.def(10)"monotonic_lt_times_r/a/span/span/
+/span class="autotactic"2span class="autotrace" trace a href="cic:/matita/arithmetics/nat/monotonic_lt_times_r.def(9)"monotonic_lt_times_r/a/span/span/
 qed.
 
 theorem lt_to_le_to_lt_times: 
@@ -702,7 +702,7 @@ theorem lt_to_le_to_lt_times:
 #n #m #p #q #ltnm #lepq #posq
 @(a href="cic:/matita/arithmetics/nat/le_to_lt_to_lt.def(4)"le_to_lt_to_lt/a ? (na title="natural times" href="cic:/fakeuri.def(1)"*/aq))
   [@a href="cic:/matita/arithmetics/nat/monotonic_le_times_r.def(8)"monotonic_le_times_r/a //
-  |@a href="cic:/matita/arithmetics/nat/monotonic_lt_times_l.def(11)"monotonic_lt_times_l/a //
+  |@a href="cic:/matita/arithmetics/nat/monotonic_lt_times_l.def(10)"monotonic_lt_times_l/a //
   ]
 qed.
 
@@ -911,7 +911,7 @@ qed.
 
 theorem le_minus_to_plus: ∀n,m,p. na title="natural minus" href="cic:/fakeuri.def(1)"-/am a title="natural 'less or equal to'" href="cic:/fakeuri.def(1)"≤/a p → na title="natural 'less or equal to'" href="cic:/fakeuri.def(1)"≤/a pa title="natural plus" href="cic:/fakeuri.def(1)"+/am.
 #n #m #p #lep @a href="cic:/matita/arithmetics/nat/transitive_le.def(3)"transitive_le/a
-  [|@a href="cic:/matita/arithmetics/nat/le_plus_minus_m_m.def(9)"le_plus_minus_m_m/a | @a href="cic:/matita/arithmetics/nat/monotonic_le_plus_l.def(6)"monotonic_le_plus_l/a // ]
+  [|@a href="cic:/matita/arithmetics/nat/le_plus_minus_m_m.def(6)"le_plus_minus_m_m/a | @a href="cic:/matita/arithmetics/nat/monotonic_le_plus_l.def(6)"monotonic_le_plus_l/a // ]
 qed.
 
 theorem le_minus_to_plus_r: ∀a,b,c. c a title="natural 'less or equal to'" href="cic:/fakeuri.def(1)"≤/a b → a a title="natural 'less or equal to'" href="cic:/fakeuri.def(1)"≤/a b a title="natural minus" href="cic:/fakeuri.def(1)"-/a c → a a title="natural plus" href="cic:/fakeuri.def(1)"+/a c a title="natural 'less or equal to'" href="cic:/fakeuri.def(1)"≤/a b.
@@ -927,7 +927,7 @@ qed.
 
 theorem lt_minus_to_plus: ∀a,b,c. a a title="natural minus" href="cic:/fakeuri.def(1)"-/a b a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a c → a a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a c a title="natural plus" href="cic:/fakeuri.def(1)"+/a b.
 #a #b #c #H @a href="cic:/matita/arithmetics/nat/not_le_to_lt.def(5)"not_le_to_lt/a 
-@(a href="cic:/matita/basics/logic/not_to_not.def(3)"not_to_not/a … (a href="cic:/matita/arithmetics/nat/lt_to_not_le.def(7)"lt_to_not_le/a …H)) /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/arithmetics/nat/le_plus_to_minus_r.def(10)"le_plus_to_minus_r/a/span/span/
+@(a href="cic:/matita/basics/logic/not_to_not.def(3)"not_to_not/a … (a href="cic:/matita/arithmetics/nat/lt_to_not_le.def(7)"lt_to_not_le/a …H)) /span class="autotactic"2span class="autotrace" trace a href="cic:/matita/arithmetics/nat/le_plus_to_minus_r.def(7)"le_plus_to_minus_r/a/span/span/
 qed.
 
 theorem lt_minus_to_plus_r: ∀a,b,c. a a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a b a title="natural minus" href="cic:/fakeuri.def(1)"-/a c → a a title="natural plus" href="cic:/fakeuri.def(1)"+/a c a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a b.
@@ -940,7 +940,7 @@ theorem lt_plus_to_minus: ∀n,m,p. m a title="natural 'less or equal to'" href
 qed.
 
 theorem lt_plus_to_minus_r: ∀a,b,c. a a title="natural plus" href="cic:/fakeuri.def(1)"+/a b a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a c → a a title="natural 'less than'" href="cic:/fakeuri.def(1)"</a c a title="natural minus" href="cic:/fakeuri.def(1)"-/a b.
-#a #b #c #H @a href="cic:/matita/arithmetics/nat/le_plus_to_minus_r.def(10)"le_plus_to_minus_r/a //
+#a #b #c #H @a href="cic:/matita/arithmetics/nat/le_plus_to_minus_r.def(7)"le_plus_to_minus_r/a //
 qed. 
 
 theorem monotonic_le_minus_r: