- ldrop is now drop as in basic_1

[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 536288f01851f0368806c06b60f49a21dddefff0..42e34097a4db92ba9d9e7bf4c3375f679b41d747 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs_lleq.ma
@@ -14,7 +14,7 @@
 
 include "basic_2/reduction/lpx_lleq.ma".
 include "basic_2/computation/cpxs_leq.ma".
-include "basic_2/computation/lpxs_ldrop.ma".
+include "basic_2/computation/lpxs_drop.ma".
 include "basic_2/computation/lpxs_cpxs.ma".
 
 (* SN EXTENDED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS ******************)
@@ -22,22 +22,22 @@ 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
 /3 width=3 by lpxs_strap1, ex2_intro/
 qed-.
 
-lemma lpxs_lleq_fqu_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83 ⦃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\83 â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+lemma lpxs_lleq_fqu_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 ⦃G2, L2, T2⦄ →
+                           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
   elim (lleq_inv_lref_ge_dx … H2 ? I L1 V1) -H2 //
-  #K1 #H #H2KL1 lapply (ldrop_inv_O2 … H) -H #H destruct
+  #K1 #H #H2KL1 lapply (drop_inv_O2 … H) -H #H destruct
   /2 width=4 by fqu_lref_O, ex3_intro/
 | * [ #a ] #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H
   [ elim (lleq_inv_bind … H)
@@ -48,20 +48,20 @@ lemma lpxs_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2,
 | #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_flat … H) -H
   /2 width=4 by fqu_flat_dx, ex3_intro/
 | #G1 #L1 #L #T1 #U1 #e #HL1 #HTU1 #K1 #H1KL1 #H2KL1
-  elim (ldrop_O1_le (e+1) K1)
+  elim (drop_O1_le (Ⓕ) (e+1) K1)
   [ #K #HK1 lapply (lleq_inv_lift_le … H2KL1 … HK1 HL1 … HTU1 ?) -H2KL1 //
-    #H2KL elim (lpxs_ldrop_trans_O1 … H1KL1 … HL1) -L1
-    #K0 #HK10 #H1KL lapply (ldrop_mono … HK10 … HK1) -HK10 #H destruct
+    #H2KL elim (lpxs_drop_trans_O1 … H1KL1 … HL1) -L1
+    #K0 #HK10 #H1KL lapply (drop_mono … HK10 … HK1) -HK10 #H destruct
     /3 width=4 by fqu_drop, ex3_intro/
-  | lapply (ldrop_fwd_length_le2 … HL1) -L -T1 -g
+  | lapply (drop_fwd_length_le2 … HL1) -L -T1 -g
     lapply (lleq_fwd_length … H2KL1) //
   ]
 ]
 qed-.
 
-lemma lpxs_lleq_fquq_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83⸮ ⦃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\83⸮ â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+lemma lpxs_lleq_fquq_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90⸮ ⦃G2, L2, T2⦄ →
+                            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
@@ -70,9 +70,9 @@ elim (fquq_inv_gen … H) -H
 ]
 qed-.
 
-lemma lpxs_lleq_fqup_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83+ ⦃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\83+ â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+lemma lpxs_lleq_fqup_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90+ ⦃G2, L2, T2⦄ →
+                            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/
@@ -82,9 +82,9 @@ lemma lpxs_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G
 ]
 qed-.
 
-lemma lpxs_lleq_fqus_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\83* ⦃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\83* â¦\83G2, K2, T2â¦\84 & â¦\83G2, K2â¦\84 â\8a¢ â\9e¡*[h, g] L2 & K2 â\8b\95[T2, 0] L2.
+lemma lpxs_lleq_fqus_trans: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 â\8a\90* ⦃G2, L2, T2⦄ →
+                            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
@@ -93,10 +93,10 @@ elim (fqus_inv_gen … H) -H
 ]
 qed-.
 
-fact leq_lpxs_trans_lleq_aux: â\88\80h,g,G,L1,L0,d,e. L1 â\89\83[d, e] L0 → e = ∞ →
+fact leq_lpxs_trans_lleq_aux: â\88\80h,g,G,L1,L0,d,e. L1 ⩬[d, e] L0 → e = ∞ →
                               ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
-                              â\88\83â\88\83L. L â\89\83[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\83â\88\83L. L ⩬[d, e] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] 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/
@@ -117,8 +117,8 @@ fact leq_lpxs_trans_lleq_aux: ∀h,g,G,L1,L0,d,e. L1 ≃[d, e] L0 → e = ∞ 
 ]
 qed-.
 
-lemma leq_lpxs_trans_lleq: â\88\80h,g,G,L1,L0,d. L1 â\89\83[d, ∞] L0 →
+lemma leq_lpxs_trans_lleq: â\88\80h,g,G,L1,L0,d. L1 ⩬[d, ∞] L0 →
                            ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
-                           â\88\83â\88\83L. L â\89\83[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\83â\88\83L. L ⩬[d, ∞] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] 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-.