update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma
index 462a000141d383e02a21298198a04b0d4552acb0..6f9b14b420483be25027fb6685a0048c7c529d8c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/reqx_fqus.ma
@@ -21,9 +21,9 @@ include "static_2/static/reqx_reqx.ma".
 
 (* Properties with extended structural successor for closures ***************)
 
-lemma fqu_teqx_conf: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82[b] â¦\83G2,L2,T1â¦\84 →
+lemma fqu_teqx_conf: â\88\80b,G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82[b] â\9dªG2,L2,T1â\9d« →
                      ∀U2. U1 ≛ U2 →
-                     â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82[b] â¦\83G2,L,T2â¦\84 & L2 ≛[T1] L & T1 ≛ T2.
+                     â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82[b] â\9dªG2,L,T2â\9d« & L2 ≛[T1] L & T1 ≛ T2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -G1 -G2 -L1 -L2 -U1 -T1
 [ #I #G #L #W #X #H >(teqx_inv_lref1 … H) -X
   /2 width=5 by fqu_lref_O, ex3_2_intro/
@@ -45,18 +45,18 @@ lemma fqu_teqx_conf: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂[b] ⦃G2,L2,T1
 ]
 qed-.
 
-lemma teqx_fqu_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82[b] â¦\83G2,L2,T1â¦\84 →
+lemma teqx_fqu_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82[b] â\9dªG2,L2,T1â\9d« →
                       ∀U2. U2 ≛ U1 →
-                      â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82[b] â¦\83G2,L,T2â¦\84 & T2 ≛ T1 & L ≛[T1] L2.
+                      â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82[b] â\9dªG2,L,T2â\9d« & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H12 #U2 #HU21
 elim (fqu_teqx_conf … H12 U2) -H12
 /3 width=5 by reqx_sym, teqx_sym, ex3_2_intro/
 qed-.
 
 (* Basic_2A1: uses: lleq_fqu_trans *)
-lemma reqx_fqu_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82[b] â¦\83G2,K2,Uâ¦\84 →
+lemma reqx_fqu_trans: â\88\80b,G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82[b] â\9dªG2,K2,Uâ\9d« →
                       ∀L1. L1 ≛[T] L2 →
-                      â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82[b] â¦\83G2,K1,U0â¦\84 & U0 ≛ U & K1 ≛[U] K2.
+                      â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82[b] â\9dªG2,K1,U0â\9d« & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H elim H -G1 -G2 -L2 -K2 -T -U
 [ #I #G #L2 #V2 #L1 #H elim (reqx_inv_zero_pair_dx … H) -H
   #K1 #V1 #HV1 #HV12 #H destruct
@@ -80,9 +80,9 @@ qed-.
 
 (* Properties with optional structural successor for closures ***************)
 
-lemma teqx_fquq_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82⸮[b] â¦\83G2,L2,T1â¦\84 →
+lemma teqx_fquq_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82⸮[b] â\9dªG2,L2,T1â\9d« →
                        ∀U2. U2 ≛ U1 →
-                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82⸮[b] â¦\83G2,L,T2â¦\84 & T2 ≛ T1 & L ≛[T1] L2.
+                       â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82⸮[b] â\9dªG2,L,T2â\9d« & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -H
 [ #H #U2 #HU21 elim (teqx_fqu_trans … H … HU21) -U1
   /3 width=5 by fqu_fquq, ex3_2_intro/
@@ -91,9 +91,9 @@ lemma teqx_fquq_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂⸮[b] ⦃G2,L2
 qed-.
 
 (* Basic_2A1: was just: lleq_fquq_trans *)
-lemma reqx_fquq_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82⸮[b] â¦\83G2,K2,Uâ¦\84 →
+lemma reqx_fquq_trans: â\88\80b,G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82⸮[b] â\9dªG2,K2,Uâ\9d« →
                        ∀L1. L1 ≛[T] L2 →
-                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82⸮[b] â¦\83G2,K1,U0â¦\84 & U0 ≛ U & K1 ≛[U] K2.
+                       â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82⸮[b] â\9dªG2,K1,U0â\9d« & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H elim H -H
 [ #H #L1 #HL12 elim (reqx_fqu_trans … H … HL12) -L2 /3 width=5 by fqu_fquq, ex3_2_intro/
 | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
@@ -103,9 +103,9 @@ qed-.
 (* Properties with plus-iterated structural successor for closures **********)
 
 (* Basic_2A1: was just: lleq_fqup_trans *)
-lemma reqx_fqup_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82+[b] â¦\83G2,K2,Uâ¦\84 →
+lemma reqx_fqup_trans: â\88\80b,G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82+[b] â\9dªG2,K2,Uâ\9d« →
                        ∀L1. L1 ≛[T] L2 →
-                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82+[b] â¦\83G2,K1,U0â¦\84 & U0 ≛ U & K1 ≛[U] K2.
+                       â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82+[b] â\9dªG2,K1,U0â\9d« & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
 [ #G2 #K2 #U #HTU #L1 #HL12 elim (reqx_fqu_trans … HTU … HL12) -L2
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -118,9 +118,9 @@ lemma reqx_fqup_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⬂+[b] ⦃G2,K2,U⦄
 ]
 qed-.
 
-lemma teqx_fqup_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82+[b] â¦\83G2,L2,T1â¦\84 →
+lemma teqx_fqup_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82+[b] â\9dªG2,L2,T1â\9d« →
                        ∀U2. U2 ≛ U1 →
-                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82+[b] â¦\83G2,L,T2â¦\84 & T2 ≛ T1 & L ≛[T1] L2.
+                       â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82+[b] â\9dªG2,L,T2â\9d« & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H @(fqup_ind_dx … H) -G1 -L1 -U1
 [ #G1 #L1 #U1 #H #U2 #HU21 elim (teqx_fqu_trans … H … HU21) -U1
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -136,9 +136,9 @@ qed-.
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma teqx_fqus_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82*[b] â¦\83G2,L2,T1â¦\84 →
+lemma teqx_fqus_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â\9dªG1,L1,U1â\9d« â¬\82*[b] â\9dªG2,L2,T1â\9d« →
                        ∀U2. U2 ≛ U1 →
-                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82*[b] â¦\83G2,L,T2â¦\84 & T2 ≛ T1 & L ≛[T1] L2.
+                       â\88\83â\88\83L,T2. â\9dªG1,L1,U2â\9d« â¬\82*[b] â\9dªG2,L,T2â\9d« & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H #U2 #HU21 elim(fqus_inv_fqup … H) -H
 [ #H elim (teqx_fqup_trans … H … HU21) -U1 /3 width=5 by fqup_fqus, ex3_2_intro/
 | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
@@ -146,9 +146,9 @@ lemma teqx_fqus_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⬂*[b] ⦃G2,L2,T
 qed-.
 
 (* Basic_2A1: was just: lleq_fqus_trans *)
-lemma reqx_fqus_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82*[b] â¦\83G2,K2,Uâ¦\84 →
+lemma reqx_fqus_trans: â\88\80b,G1,G2,L2,K2,T,U. â\9dªG1,L2,Tâ\9d« â¬\82*[b] â\9dªG2,K2,Uâ\9d« →
                        ∀L1. L1 ≛[T] L2 →
-                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82*[b] â¦\83G2,K1,U0â¦\84 & U0 ≛ U & K1 ≛[U] K2.
+                       â\88\83â\88\83K1,U0. â\9dªG1,L1,Tâ\9d« â¬\82*[b] â\9dªG2,K1,U0â\9d« & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_fqup … H) -H
 [ #H elim (reqx_fqup_trans … H … HL12) -L2 /3 width=5 by fqup_fqus, ex3_2_intro/
 | * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/