renaming

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfdeq_fqus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_fqus.ma
index 78345ad1e7fcdb6966037683271f9cd4eca812c6..84685ca10739233e6b337cc765bd1a22f85bdef8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_fqus.ma
@@ -19,11 +19,11 @@ include "basic_2/static/lfdeq_lfdeq.ma".
 
 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
 
-(* Properties with supclosure ***********************************************)
+(* Properties with extended structural successor for closures ***************)
 
 lemma fqu_tdeq_conf: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, T1⦄ →
-                     â\88\80U2. U1 â\89¡[h, o] U2 →
-                     â\88\83â\88\83L,T2. â¦\83G1, L1, U2â¦\84 â\8a\90[b] â¦\83G2, L, T2â¦\84 & L2 â\89¡[h, o, T1] L & T1 â\89¡[h, o] T2.
+                     â\88\80U2. U1 â\89\9b[h, o] U2 →
+                     â\88\83â\88\83L,T2. â¦\83G1, L1, U2â¦\84 â\8a\90[b] â¦\83G2, L, T2â¦\84 & L2 â\89\9b[h, o, T1] L & T1 â\89\9b[h, o] T2.
 #h #o #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/
@@ -32,7 +32,7 @@ lemma fqu_tdeq_conf: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐[b] ⦃G2,
   /2 width=5 by fqu_pair_sn, ex3_2_intro/
 | #p #I #G #L #W1 #U1 #X #H
   elim (tdeq_inv_pair1 … H) -H #W2 #U2 #HW12 #HU12 #H destruct
-  /3 width=5 by lfdeq_pair, fqu_bind_dx, ex3_2_intro/
+  /3 width=5 by lfdeq_pair_refl, fqu_bind_dx, ex3_2_intro/
 | #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 fqu_clear, ex3_2_intro/
@@ -46,21 +46,21 @@ lemma fqu_tdeq_conf: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐[b] ⦃G2,
 qed-.
 
 lemma tdeq_fqu_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, T1⦄ →
-                      â\88\80U2. U2 â\89¡[h, o] U1 →
-                      â\88\83â\88\83L,T2. â¦\83G1, L1, U2â¦\84 â\8a\90[b] â¦\83G2, L, T2â¦\84 & T2 â\89¡[h, o] T1 & L â\89¡[h, o, T1] L2.
+                      â\88\80U2. U2 â\89\9b[h, o] U1 →
+                      â\88\83â\88\83L,T2. â¦\83G1, L1, U2â¦\84 â\8a\90[b] â¦\83G2, L, T2â¦\84 & T2 â\89\9b[h, o] T1 & L â\89\9b[h, o, T1] L2.
 #h #o #b #G1 #G2 #L1 #L2 #U1 #T1 #H12 #U2 #HU21
 elim (fqu_tdeq_conf … o … H12 U2) -H12
 /3 width=5 by lfdeq_sym, tdeq_sym, ex3_2_intro/
 qed-.
 
-(* Basic_2A1: was just: lleq_fqu_trans *)
+(* Basic_2A1: uses: lleq_fqu_trans *)
 lemma lfdeq_fqu_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐[b] ⦃G2, K2, U⦄ →
-                       â\88\80L1. L1 â\89¡[h, o, T] L2 →
-                       â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90[b] â¦\83G2, K1, U0â¦\84 & U0 â\89¡[h, o] U & K1 â\89¡[h, o, U] K2.
+                       â\88\80L1. L1 â\89\9b[h, o, T] L2 →
+                       â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90[b] â¦\83G2, K1, U0â¦\84 & U0 â\89\9b[h, o] U & K1 â\89\9b[h, o, U] K2.
 #h #o #b #G1 #G2 #L2 #K2 #T #U #H elim H -G1 -G2 -L2 -K2 -T -U
 [ #I #G #L2 #V2 #L1 #H elim (lfdeq_inv_zero_pair_dx … H) -H
   #K1 #V1 #HV1 #HV12 #H destruct
-  /3 width=7 by tdeq_lfdeq_conf_sn, fqu_lref_O, ex3_2_intro/
+  /3 width=7 by tdeq_lfdeq_conf, fqu_lref_O, ex3_2_intro/
 | * [ #p ] #I #G #L2 #V #T #L1 #H
   [ elim (lfdeq_inv_bind … H)
   | elim (lfdeq_inv_flat … H)
@@ -78,20 +78,34 @@ lemma lfdeq_fqu_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐[b] ⦃G2, K
 ]
 qed-.
 
+(* Properties with optional structural successor for closures ***************)
+
+lemma tdeq_fquq_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, T1⦄ →
+                       ∀U2. U2 ≛[h, o] U1 →
+                       ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐⸮[b] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
+#h #o #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/
+| * #HG #HL #HT destruct /2 width=5 by ex3_2_intro/
+]
+qed-.
+
 (* Basic_2A1: was just: lleq_fquq_trans *)
 lemma lfdeq_fquq_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐⸮[b] ⦃G2, K2, U⦄ →
-                        â\88\80L1. L1 â\89¡[h, o, T] L2 →
-                        â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90⸮[b] â¦\83G2, K1, U0â¦\84 & U0 â\89¡[h, o] U & K1 â\89¡[h, o, U] K2.
+                        â\88\80L1. L1 â\89\9b[h, o, T] L2 →
+                        â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90⸮[b] â¦\83G2, K1, U0â¦\84 & U0 â\89\9b[h, o] U & K1 â\89\9b[h, o, U] K2.
 #h #o #b #G1 #G2 #L2 #K2 #T #U #H elim H -H
 [ #H #L1 #HL12 elim (lfdeq_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/
 ]
 qed-.
 
+(* Properties with plus-iterated structural successor for closures **********)
+
 (* Basic_2A1: was just: lleq_fqup_trans *)
 lemma lfdeq_fqup_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐+[b] ⦃G2, K2, U⦄ →
-                        â\88\80L1. L1 â\89¡[h, o, T] L2 →
-                        â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90+[b] â¦\83G2, K1, U0â¦\84 & U0 â\89¡[h, o] U & K1 â\89¡[h, o, U] K2.
+                        â\88\80L1. L1 â\89\9b[h, o, T] L2 →
+                        â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90+[b] â¦\83G2, K1, U0â¦\84 & U0 â\89\9b[h, o] U & K1 â\89\9b[h, o, U] K2.
 #h #o #b #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
 [ #G2 #K2 #U #HTU #L1 #HL12 elim (lfdeq_fqu_trans … HTU … HL12) -L2
   /3 width=5 by fqu_fqup, ex3_2_intro/
@@ -100,14 +114,41 @@ lemma lfdeq_fqup_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐+[b] ⦃G2,
   elim (lfdeq_fqu_trans … HU2 … HK0) -K #K1 #U1 #HU1 #HU12 #HK12
   elim (tdeq_fqu_trans … HU1 … HU0) -U #K3 #U3 #HU03 #HU31 #HK31
   @(ex3_2_intro … K3 U3) (**) (* full auto too slow *)
-  /3 width=5 by lfdeq_trans, tdeq_lfdeq_conf_sn, fqup_strap1, tdeq_trans/
+  /3 width=5 by lfdeq_trans, tdeq_lfdeq_conf, fqup_strap1, tdeq_trans/
+]
+qed-.
+
+lemma tdeq_fqup_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, T1⦄ →
+                       ∀U2. U2 ≛[h, o] U1 →
+                       ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐+[b] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
+#h #o #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/
+| #G1 #G #L1 #L #U1 #U #H #_ #IH #U2 #HU21
+  elim (tdeq_fqu_trans … H … HU21) -U1 #L0 #T #H1 #HTU #HL0
+  lapply (tdeq_lfdeq_div … HTU … HL0) -HL0 #HL0
+  elim (IH … HTU) -U #K2 #U1 #H2 #HUT1 #HKL2
+  elim (lfdeq_fqup_trans … H2 … HL0) -L #K #U #H2 #HU1 #HK2
+  lapply (tdeq_lfdeq_conf … HUT1 … HK2) -HK2 #HK2
+  /3 width=7 by lfdeq_trans, fqup_strap2, tdeq_trans, ex3_2_intro/
+]
+qed-.
+
+(* Properties with star-iterated structural successor for closures **********)
+
+lemma tdeq_fqus_trans: ∀h,o,b,G1,G2,L1,L2,U1,T1. ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, T1⦄ →
+                       ∀U2. U2 ≛[h, o] U1 →
+                       ∃∃L,T2. ⦃G1, L1, U2⦄ ⊐*[b] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
+#h #o #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/
 ]
 qed-.
 
 (* Basic_2A1: was just: lleq_fqus_trans *)
 lemma lfdeq_fqus_trans: ∀h,o,b,G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊐*[b] ⦃G2, K2, U⦄ →
-                        â\88\80L1. L1 â\89¡[h, o, T] L2 →
-                        â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90*[b] â¦\83G2, K1, U0â¦\84 & U0 â\89¡[h, o] U & K1 â\89¡[h, o, U] K2.
+                        â\88\80L1. L1 â\89\9b[h, o, T] L2 →
+                        â\88\83â\88\83K1,U0. â¦\83G1, L1, Tâ¦\84 â\8a\90*[b] â¦\83G2, K1, U0â¦\84 & U0 â\89\9b[h, o] U & K1 â\89\9b[h, o, U] K2.
 #h #o #b #G1 #G2 #L2 #K2 #T #U #H #L1 #HL12 elim(fqus_inv_fqup … H) -H
 [ #H elim (lfdeq_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/