- advances in the theory of cofrees

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lpxs_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma
index 8f48afe864a053eb82b207be15bf28fe77e5e5f7..4263c55cd78aefe29a725e44de525de6de27ca2a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma
@@ -22,8 +22,8 @@ include "basic_2/computation/lpxs_cpxs.ma".
 (* Properties on lazy equivalence for local environments ********************)
 
 lemma lleq_lpxs_trans: ∀h,g,G,L2,K2. ⦃G, L2⦄ ⊢ ➡*[h, g] K2 →
-                       â\88\80L1,T,d. L1 â\8b\95[T, d] L2 →
-                       â\88\83â\88\83K1. â¦\83G, L1â¦\84 â\8a¢ â\9e¡*[h, g] K1 & K1 â\8b\95[T, d] K2.
+                       â\88\80L1,T,d. L1 â\89¡[T, d] L2 →
+                       â\88\83â\88\83K1. â¦\83G, L1â¦\84 â\8a¢ â\9e¡*[h, g] K1 & K1 â\89¡[T, d] K2.
 #h #g #G #L2 #K2 #H @(lpxs_ind … H) -K2 /2 width=3 by ex2_intro/
 #K #K2 #_ #HK2 #IH #L1 #T #d #HT elim (IH … HT) -L2
 #L #HL1 #HT elim (lleq_lpx_trans … HK2 … HT) -K
@@ -31,8 +31,8 @@ lemma lleq_lpxs_trans: ∀h,g,G,L2,K2. ⦃G, L2⦄ ⊢ ➡*[h, g] K2 →
 qed-.
 
 lemma lpxs_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                           â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\8b\95[T1, 0] L1 →
-                           â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90 â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+                           â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\89¡[T1, 0] L1 →
+                           â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90 â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\89¡[T2, 0] L2.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
 [ #I #G1 #L1 #V1 #X #H1 #H2 elim (lpxs_inv_pair2 … H1) -H1
   #K0 #V0 #H1KL1 #_ #H destruct
@@ -60,8 +60,8 @@ lemma lpxs_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2,
 qed-.
 
 lemma lpxs_lleq_fquq_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                            â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\8b\95[T1, 0] L1 →
-                            â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90⸮ â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+                            â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\89¡[T1, 0] L1 →
+                            â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90⸮ â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\89¡[T2, 0] L2.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
 elim (fquq_inv_gen … H) -H
 [ #H elim (lpxs_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
@@ -71,8 +71,8 @@ elim (fquq_inv_gen … H) -H
 qed-.
 
 lemma lpxs_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                            â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\8b\95[T1, 0] L1 →
-                            â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90+ â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+                            â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\89¡[T1, 0] L1 →
+                            â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90+ â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\89¡[T2, 0] L2.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 [ #G2 #L2 #T2 #H #K1 #H1KL1 #H2KL1 elim (lpxs_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -83,8 +83,8 @@ lemma lpxs_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G
 qed-.
 
 lemma lpxs_lleq_fqus_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                            â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\8b\95[T1, 0] L1 →
-                            â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90* â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+                            â\88\80K1. â¦\83G1, K1â¦\84 â\8a¢ â\9e¡*[h, g] L1 â\86\92 K1 â\89¡[T1, 0] L1 →
+                            â\88\83â\88\83K2. â¦\83G1, K1, T1â¦\84 â\8a\90* â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\89¡[T2, 0] L2.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
 elim (fqus_inv_gen … H) -H
 [ #H elim (lpxs_lleq_fqup_trans … H … H1KL1 H2KL1) -L1
@@ -96,7 +96,7 @@ qed-.
 fact leq_lpxs_trans_lleq_aux: ∀h,g,G,L1,L0,d,e. L1 ≃[d, e] L0 → e = ∞ →
                               ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
                               ∃∃L. L ≃[d, e] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
-                                   (â\88\80T. L0 â\8b\95[T, d] L2 â\86\94 L1 â\8b\95[T, d] L).
+                                   (â\88\80T. L0 â\89¡[T, d] L2 â\86\94 L1 â\89¡[T, d] L).
 #h #g #G #L1 #L0 #d #e #H elim H -L1 -L0 -d -e
 [ #d #e #_ #L2 #H >(lpxs_inv_atom1 … H) -H
   /3 width=5 by ex3_intro, conj/
@@ -120,5 +120,5 @@ qed-.
 lemma leq_lpxs_trans_lleq: ∀h,g,G,L1,L0,d. L1 ≃[d, ∞] L0 →
                            ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
                            ∃∃L. L ≃[d, ∞] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
-                                (â\88\80T. L0 â\8b\95[T, d] L2 â\86\94 L1 â\8b\95[T, d] L).
+                                (â\88\80T. L0 â\89¡[T, d] L2 â\86\94 L1 â\89¡[T, d] L).
 /2 width=1 by leq_lpxs_trans_lleq_aux/ qed-.