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[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_fqus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
index 5fc7879fe914ec680979067d24a43228a8124395..eb8e6748ac386f51411fddb8c9dc00ecd1bae6ab 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
@@ -22,32 +22,32 @@ include "basic_2/rt_computation/cpxs_cpxs.ma".
 (* Properties on supclosure *************************************************)
 
 lemma fqu_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 →
-                      â\88\80T1. â¦\83G1,L1,T1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
-                      â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â\8a\90[b] ⦃G2,L2,U2⦄.
+                      â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
+                      â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqu_cpx_trans … HT1 … HT2) -T
 #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
 lemma fquq_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 →
-                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â\8a\90⸮[b] ⦃G2,L2,T2⦄ →
-                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â\8a\90⸮[b] ⦃G2,L2,U2⦄.
+                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82⸮[b] ⦃G2,L2,T2⦄ →
+                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82⸮[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fquq_cpx_trans … HT1 … HT2) -T
 #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
 lemma fqup_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 →
-                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â\8a\90+[b] ⦃G2,L2,T2⦄ →
-                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â\8a\90+[b] ⦃G2,L2,U2⦄.
+                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82+[b] ⦃G2,L2,T2⦄ →
+                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82+[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqup_cpx_trans … HT1 … HT2) -T
 #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
 lemma fqus_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 →
-                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â\8a\90*[b] ⦃G2,L2,T2⦄ →
-                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â\8a\90*[b] ⦃G2,L2,U2⦄.
+                       â\88\80T1. â¦\83G1,L1,T1â¦\84 â¬\82*[b] ⦃G2,L2,T2⦄ →
+                       â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & â¦\83G1,L1,U1â¦\84 â¬\82*[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqus_cpx_trans … HT1 … HT2) -T
 #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
@@ -55,9 +55,9 @@ qed-.
 
 (* Note: a proof based on fqu_cpx_trans_tdneq might exist *)
 (* Basic_2A1: uses: fqu_cpxs_trans_neq *)
-lemma fqu_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90[b] ⦃G2,L2,T2⦄ →
+lemma fqu_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82[b] ⦃G2,L2,T2⦄ →
                             ∀U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛ U2 → ⊥) →
-                            â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â\8a\90[b] ⦃G2,L2,U2⦄.
+                            â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G #L #V1 #V2 #HV12 #_ elim (lifts_total V2 𝐔❴1❵)
   #U2 #HVU2 @(ex3_intro … U2)
@@ -69,7 +69,7 @@ lemma fqu_cpxs_trans_tdneq: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G
   [1,3: /2 width=4 by fqu_pair_sn, cpxs_pair_sn/
   | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
   ]
-| #p #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2))
+| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2))
   [1,3: /2 width=4 by fqu_bind_dx, cpxs_bind/
   | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
   ]
@@ -88,9 +88,9 @@ lemma fqu_cpxs_trans_tdneq: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐[b] ⦃G
 qed-.
 
 (* Basic_2A1: uses: fquq_cpxs_trans_neq *)
-lemma fquq_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90⸮[b] ⦃G2,L2,T2⦄ →
+lemma fquq_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82⸮[b] ⦃G2,L2,T2⦄ →
                              ∀U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛ U2 → ⊥) →
-                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â\8a\90⸮[b] ⦃G2,L2,U2⦄.
+                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82⸮[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12
 [ #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_tdneq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
@@ -99,9 +99,9 @@ lemma fquq_cpxs_trans_tdneq: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐⸮[b]
 qed-.
 
 (* Basic_2A1: uses: fqup_cpxs_trans_neq *)
-lemma fqup_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90+[b] ⦃G2,L2,T2⦄ →
+lemma fqup_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82+[b] ⦃G2,L2,T2⦄ →
                              ∀U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛ U2 → ⊥) →
-                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â\8a\90+[b] ⦃G2,L2,U2⦄.
+                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82+[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
 [ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_tdneq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -112,9 +112,9 @@ lemma fqup_cpxs_trans_tdneq: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐+[b] 
 qed-.
 
 (* Basic_2A1: uses: fqus_cpxs_trans_neq *)
-lemma fqus_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90*[b] ⦃G2,L2,T2⦄ →
+lemma fqus_cpxs_trans_tdneq: â\88\80h,b,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82*[b] ⦃G2,L2,T2⦄ →
                              ∀U2. ⦃G2,L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≛ U2 → ⊥) →
-                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â\8a\90*[b] ⦃G2,L2,U2⦄.
+                             â\88\83â\88\83U1. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] U1 & T1 â\89\9b U1 â\86\92 â\8a¥ & â¦\83G1,L1,U1â¦\84 â¬\82*[b] ⦃G2,L2,U2⦄.
 #h #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12
 [ #H12 elim (fqup_cpxs_trans_tdneq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/