update in ground static_2 basic_2 apps_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / reqg_fqus.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqg_fqus.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqg_fqus.ma
index 55e23580afe8572134fc5773c8c261d994cbd25a..a802044f868be698dbfaeda8a7969644ae033aa3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/reqg_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/reqg_fqus.ma
@@ -23,9 +23,9 @@ include "static_2/static/reqg_reqg.ma".
 
 lemma fqu_teqg_conf (S) (b):
       reflexive … S →
-      â\88\80G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82[b] â\9dªG2,L2,T1â\9d« →
+      â\88\80G1,G2,L1,L2,U1,T1. â\9d¨G1,L1,U1â\9d© â¬\82[b] â\9d¨G2,L2,T1â\9d© →
       ∀U2. U1 ≛[S] U2 →
-      â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82[b] â\9dªG2,L,T2â\9d« & L2 ≛[S,T1] L & T1 ≛[S] T2.
+      â\88\83â\88\83L,T2. â\9d¨G1,L1,U2â\9d© â¬\82[b] â\9d¨G2,L,T2â\9d© & L2 ≛[S,T1] L & T1 ≛[S] T2.
 #S #b #HS #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -G1 -G2 -L1 -L2 -U1 -T1
 [ #I #G #L #W #X #H >(teqg_inv_lref1 … H) -X
   /3 width=5 by reqg_refl, fqu_lref_O, teqg_refl, ex3_2_intro/
@@ -49,9 +49,9 @@ qed-.
 
 lemma teqg_fqu_trans (S) (b):
       reflexive … S → symmetric … S →
-      â\88\80G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82[b] â\9dªG2,L2,T1â\9d« →
+      â\88\80G1,G2,L1,L2,U1,T1. â\9d¨G1,L1,U1â\9d© â¬\82[b] â\9d¨G2,L2,T1â\9d© →
       ∀U2. U2 ≛[S] U1 →
-      â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82[b] â\9dªG2,L,T2â\9d« & T2 ≛[S] T1 & L ≛[S,T1] L2.
+      â\88\83â\88\83L,T2. â\9d¨G1,L1,U2â\9d© â¬\82[b] â\9d¨G2,L,T2â\9d© & T2 ≛[S] T1 & L ≛[S,T1] L2.
 #S #b #H1S #H2S #G1 #G2 #L1 #L2 #U1 #T1 #H12 #U2 #HU21
 elim (fqu_teqg_conf … H12 U2) -H12
 /3 width=5 by reqg_sym, teqg_sym, ex3_2_intro/
@@ -60,9 +60,9 @@ qed-.
 (* Basic_2A1: uses: lleq_fqu_trans *)
 lemma reqg_fqu_trans (S) (b):
       reflexive … S →
-      â\88\80G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82[b] â\9dªG2,K2,Uâ\9d« →
+      â\88\80G1,G2,L2,K2,T,U. â\9d¨G1,L2,Tâ\9d© â¬\82[b] â\9d¨G2,K2,Uâ\9d© →
       ∀L1. L1 ≛[S,T] L2 →
-      â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82[b] â\9dªG2,K1,U0â\9d« & U0 ≛[S] U & K1 ≛[S,U] K2.
+      â\88\83â\88\83K1,U0. â\9d¨G1,L1,Tâ\9d© â¬\82[b] â\9d¨G2,K1,U0â\9d© & U0 ≛[S] U & K1 ≛[S,U] K2.
 #S #b #HS #G1 #G2 #L2 #K2 #T #U #H elim H -G1 -G2 -L2 -K2 -T -U
 [ #I #G #L2 #V2 #L1 #H elim (reqg_inv_zero_pair_dx … H) -H
   #K1 #V1 #HV1 #HV12 #H destruct
@@ -88,9 +88,9 @@ qed-.
 
 lemma teqg_fquq_trans (S) (b):
       reflexive … S → symmetric … S →
-      â\88\80G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,T1â\9d« →
+      â\88\80G1,G2,L1,L2,U1,T1. â\9d¨G1,L1,U1â\9d© â¬\82⸮[b] â\9d¨G2,L2,T1â\9d© →
       ∀U2. U2 ≛[S] U1 →
-      â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82⸮[b] â\9dªG2,L,T2â\9d« & T2 ≛[S] T1 & L ≛[S,T1] L2.
+      â\88\83â\88\83L,T2. â\9d¨G1,L1,U2â\9d© â¬\82⸮[b] â\9d¨G2,L,T2â\9d© & T2 ≛[S] T1 & L ≛[S,T1] L2.
 #S #b #H1S #H2S #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -H
 [ #H #U2 #HU21 elim (teqg_fqu_trans … H … HU21) -U1
   /3 width=5 by fqu_fquq, ex3_2_intro/
@@ -101,9 +101,9 @@ qed-.
 (* Basic_2A1: was just: lleq_fquq_trans *)
 lemma reqg_fquq_trans (S) (b):
       reflexive … S →
-      â\88\80G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82⸮[b] â\9dªG2,K2,Uâ\9d« →
+      â\88\80G1,G2,L2,K2,T,U. â\9d¨G1,L2,Tâ\9d© â¬\82⸮[b] â\9d¨G2,K2,Uâ\9d© →
       ∀L1. L1 ≛[S,T] L2 →
-      â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82⸮[b] â\9dªG2,K1,U0â\9d« & U0 ≛[S] U & K1 ≛[S,U] K2.
+      â\88\83â\88\83K1,U0. â\9d¨G1,L1,Tâ\9d© â¬\82⸮[b] â\9d¨G2,K1,U0â\9d© & U0 ≛[S] U & K1 ≛[S,U] K2.
 #S #b #HS #G1 #G2 #L2 #K2 #T #U #H elim H -H
 [ #H #L1 #HL12 elim (reqg_fqu_trans … H … HL12) -L2 /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #HG #HL #HT destruct /3 width=5 by teqg_refl, ex3_2_intro/
@@ -115,9 +115,9 @@ qed-.
 (* Basic_2A1: was just: lleq_fqup_trans *)
 lemma reqg_fqup_trans (S) (b):
       reflexive … S → symmetric … S → Transitive … S →
-      â\88\80G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82+[b] â\9dªG2,K2,Uâ\9d« →
+      â\88\80G1,G2,L2,K2,T,U. â\9d¨G1,L2,Tâ\9d© â¬\82+[b] â\9d¨G2,K2,Uâ\9d© →
       ∀L1. L1 ≛[S,T] L2 →
-      â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82+[b] â\9dªG2,K1,U0â\9d« & U0 ≛[S] U & K1 ≛[S,U] K2.
+      â\88\83â\88\83K1,U0. â\9d¨G1,L1,Tâ\9d© â¬\82+[b] â\9d¨G2,K1,U0â\9d© & U0 ≛[S] U & K1 ≛[S,U] K2.
 #S #b #H1S #H2S #H3S #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
 [ #G2 #K2 #U #HTU #L1 #HL12 elim (reqg_fqu_trans … HTU … HL12) -L2
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -132,9 +132,9 @@ qed-.
 
 lemma teqg_fqup_trans (S) (b):
       reflexive … S → symmetric … S → Transitive … S →
-      â\88\80G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82+[b] â\9dªG2,L2,T1â\9d« →
+      â\88\80G1,G2,L1,L2,U1,T1. â\9d¨G1,L1,U1â\9d© â¬\82+[b] â\9d¨G2,L2,T1â\9d© →
       ∀U2. U2 ≛[S] U1 →
-      â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82+[b] â\9dªG2,L,T2â\9d« & T2 ≛[S] T1 & L ≛[S,T1] L2.
+      â\88\83â\88\83L,T2. â\9d¨G1,L1,U2â\9d© â¬\82+[b] â\9d¨G2,L,T2â\9d© & T2 ≛[S] T1 & L ≛[S,T1] L2.
 #S #b #H1S #H2S #H3S #G1 #G2 #L1 #L2 #U1 #T1 #H @(fqup_ind_dx … H) -G1 -L1 -U1
 [ #G1 #L1 #U1 #H #U2 #HU21 elim (teqg_fqu_trans … H … HU21) -U1 //
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -152,9 +152,9 @@ qed-.
 
 lemma teqg_fqus_trans (S) (b):
       reflexive … S → symmetric … S → Transitive … S →
-      â\88\80G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82*[b] â\9dªG2,L2,T1â\9d« →
+      â\88\80G1,G2,L1,L2,U1,T1. â\9d¨G1,L1,U1â\9d© â¬\82*[b] â\9d¨G2,L2,T1â\9d© →
       ∀U2. U2 ≛[S] U1 →
-      â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82*[b] â\9dªG2,L,T2â\9d« & T2 ≛[S] T1 & L ≛[S,T1] L2.
+      â\88\83â\88\83L,T2. â\9d¨G1,L1,U2â\9d© â¬\82*[b] â\9d¨G2,L,T2â\9d© & T2 ≛[S] T1 & L ≛[S,T1] L2.
 #S #b #H1S #H2S #H3S #G1 #G2 #L1 #L2 #U1 #T1 #H #U2 #HU21 elim(fqus_inv_fqup … H) -H
 [ #H elim (teqg_fqup_trans … H … HU21) -U1 /3 width=5 by fqup_fqus, ex3_2_intro/
 | * #HG #HL #HT destruct /3 width=5 by reqg_refl, ex3_2_intro/
@@ -164,9 +164,9 @@ qed-.
 (* Basic_2A1: was just: lleq_fqus_trans *)
 lemma reqg_fqus_trans (S) (b):
       reflexive … S → symmetric … S → Transitive … S →
-      â\88\80G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82*[b] â\9dªG2,K2,Uâ\9d« →
+      â\88\80G1,G2,L2,K2,T,U. â\9d¨G1,L2,Tâ\9d© â¬\82*[b] â\9d¨G2,K2,Uâ\9d© →
       ∀L1. L1 ≛[S,T] L2 →
-      â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82*[b] â\9dªG2,K1,U0â\9d« & U0 ≛[S] U & K1 ≛[S,U] K2.
+      â\88\83â\88\83K1,U0. â\9d¨G1,L1,Tâ\9d© â¬\82*[b] â\9d¨G2,K1,U0â\9d© & U0 ≛[S] U & K1 ≛[S,U] K2.
 #S #b #H1S #H2S #H3S #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_fqup … H) -H
 [ #H elim (reqg_fqup_trans … H … HL12) -L2 /3 width=5 by fqup_fqus, ex3_2_intro/
 | * #HG #HL #HT destruct /3 width=5 by teqg_refl, ex3_2_intro/