more additions and corrections for the article

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rdeq_fqus.ma b/matita/matita/contribs/lambdadelta/static_2/static/rdeq_fqus.ma
index bbd8a38212232c4a918cbf637c0a23bbb140f37a..d698643907a3f39eec559c3283dbbbfdbc278947 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rdeq_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rdeq_fqus.ma
@@ -21,16 +21,16 @@ include "static_2/static/rdeq_rdeq.ma".
 
 (* Properties with extended structural successor for closures ***************)
 
-lemma fqu_tdeq_conf: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â\8a\90[b] ⦃G2,L2,T1⦄ →
+lemma fqu_tdeq_conf: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82[b] ⦃G2,L2,T1⦄ →
                      ∀U2. U1 ≛ U2 →
-                     â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â\8a\90[b] ⦃G2,L,T2⦄ & L2 ≛[T1] L & T1 ≛ T2.
+                     â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82[b] ⦃G2,L,T2⦄ & 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 >(tdeq_inv_lref1 … H) -X
   /2 width=5 by fqu_lref_O, ex3_2_intro/
 | #I #G #L #W1 #U1 #X #H
   elim (tdeq_inv_pair1 … H) -H #W2 #U2 #HW12 #_ #H destruct
   /2 width=5 by fqu_pair_sn, ex3_2_intro/
-| #p #I #G #L #W1 #U1 #X #H
+| #p #I #G #L #W1 #U1 #Hb #X #H
   elim (tdeq_inv_pair1 … H) -H #W2 #U2 #HW12 #HU12 #H destruct
   /3 width=5 by rdeq_pair_refl, fqu_bind_dx, ex3_2_intro/
 | #p #I #G #L #W1 #U1 #Hb #X #H
@@ -45,18 +45,18 @@ lemma fqu_tdeq_conf: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⊐[b] ⦃G2,L2,T1
 ]
 qed-.
 
-lemma tdeq_fqu_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â\8a\90[b] ⦃G2,L2,T1⦄ →
+lemma tdeq_fqu_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82[b] ⦃G2,L2,T1⦄ →
                       ∀U2. U2 ≛ U1 →
-                      â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â\8a\90[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
+                      â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H12 #U2 #HU21
 elim (fqu_tdeq_conf … H12 U2) -H12
 /3 width=5 by rdeq_sym, tdeq_sym, ex3_2_intro/
 qed-.
 
 (* Basic_2A1: uses: lleq_fqu_trans *)
-lemma rdeq_fqu_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â\8a\90[b] ⦃G2,K2,U⦄ →
+lemma rdeq_fqu_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82[b] ⦃G2,K2,U⦄ →
                       ∀L1. L1 ≛[T] L2 →
-                      â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â\8a\90[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2.
+                      â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82[b] ⦃G2,K1,U0⦄ & 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 (rdeq_inv_zero_pair_dx … H) -H
   #K1 #V1 #HV1 #HV12 #H destruct
@@ -66,8 +66,8 @@ lemma rdeq_fqu_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⊐[b] ⦃G2,K2,U⦄ 
   | elim (rdeq_inv_flat … H)
   ] -H
   /2 width=5 by fqu_pair_sn, ex3_2_intro/
-| #p #I #G #L2 #V #T #L1 #H elim (rdeq_inv_bind … H) -H
-  /2 width=5 by fqu_bind_dx, ex3_2_intro/
+| #p #I #G #L2 #V #T #Hb #L1 #H elim (rdeq_inv_bind … H) -H
+  /3 width=5 by fqu_bind_dx, ex3_2_intro/
 | #p #I #G #L2 #V #T #Hb #L1 #H elim (rdeq_inv_bind_void … H) -H
   /3 width=5 by fqu_clear, ex3_2_intro/
 | #I #G #L2 #V #T #L1 #H elim (rdeq_inv_flat … H) -H
@@ -80,9 +80,9 @@ qed-.
 
 (* Properties with optional structural successor for closures ***************)
 
-lemma tdeq_fquq_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â\8a\90⸮[b] ⦃G2,L2,T1⦄ →
+lemma tdeq_fquq_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82⸮[b] ⦃G2,L2,T1⦄ →
                        ∀U2. U2 ≛ U1 →
-                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â\8a\90⸮[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
+                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82⸮[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H elim H -H
 [ #H #U2 #HU21 elim (tdeq_fqu_trans … H … HU21) -U1
   /3 width=5 by fqu_fquq, ex3_2_intro/
@@ -91,9 +91,9 @@ lemma tdeq_fquq_trans: ∀b,G1,G2,L1,L2,U1,T1. ⦃G1,L1,U1⦄ ⊐⸮[b] ⦃G2,L2
 qed-.
 
 (* Basic_2A1: was just: lleq_fquq_trans *)
-lemma rdeq_fquq_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â\8a\90⸮[b] ⦃G2,K2,U⦄ →
+lemma rdeq_fquq_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82⸮[b] ⦃G2,K2,U⦄ →
                        ∀L1. L1 ≛[T] L2 →
-                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â\8a\90⸮[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2.
+                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82⸮[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H elim H -H
 [ #H #L1 #HL12 elim (rdeq_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 rdeq_fqup_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â\8a\90+[b] ⦃G2,K2,U⦄ →
+lemma rdeq_fqup_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82+[b] ⦃G2,K2,U⦄ →
                        ∀L1. L1 ≛[T] L2 →
-                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â\8a\90+[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2.
+                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82+[b] ⦃G2,K1,U0⦄ & 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 (rdeq_fqu_trans … HTU … HL12) -L2
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -118,9 +118,9 @@ lemma rdeq_fqup_trans: ∀b,G1,G2,L2,K2,T,U. ⦃G1,L2,T⦄ ⊐+[b] ⦃G2,K2,U⦄
 ]
 qed-.
 
-lemma tdeq_fqup_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â\8a\90+[b] ⦃G2,L2,T1⦄ →
+lemma tdeq_fqup_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82+[b] ⦃G2,L2,T1⦄ →
                        ∀U2. U2 ≛ U1 →
-                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â\8a\90+[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
+                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82+[b] ⦃G2,L,T2⦄ & 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 (tdeq_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 tdeq_fqus_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â\8a\90*[b] ⦃G2,L2,T1⦄ →
+lemma tdeq_fqus_trans: â\88\80b,G1,G2,L1,L2,U1,T1. â¦\83G1,L1,U1â¦\84 â¬\82*[b] ⦃G2,L2,T1⦄ →
                        ∀U2. U2 ≛ U1 →
-                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â\8a\90*[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
+                       â\88\83â\88\83L,T2. â¦\83G1,L1,U2â¦\84 â¬\82*[b] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
 #b #G1 #G2 #L1 #L2 #U1 #T1 #H #U2 #HU21 elim(fqus_inv_fqup … H) -H
 [ #H elim (tdeq_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 tdeq_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 rdeq_fqus_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â\8a\90*[b] ⦃G2,K2,U⦄ →
+lemma rdeq_fqus_trans: â\88\80b,G1,G2,L2,K2,T,U. â¦\83G1,L2,Tâ¦\84 â¬\82*[b] ⦃G2,K2,U⦄ →
                        ∀L1. L1 ≛[T] L2 →
-                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â\8a\90*[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2.
+                       â\88\83â\88\83K1,U0. â¦\83G1,L1,Tâ¦\84 â¬\82*[b] ⦃G2,K1,U0⦄ & U0 ≛ U & K1 ≛[U] K2.
 #b #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_fqup … H) -H
 [ #H elim (rdeq_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/