- improved definition of lsx allows more invariants

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / lpx_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
index b54c386b99f454a821191d06116017fb47109b5d..9daa4465616fe3f70ab4a7828f5f273d7455bd8c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_lleq.ma
@@ -1,18 +1,57 @@
-include "basic_2/relocation/lleq_lleq.ma".
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/substitution/lleq_ext.ma".
 include "basic_2/reduction/lpx_ldrop.ma".
 
 (* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
 
 (* Properties on lazy equivalence for local environments ********************)
+(*
+lamma pippo: ∀h,g,G,L2,K2. ⦃G, L2⦄ ⊢ ➡[h, g] K2 → ∀L1. |L1| = |L2| →
+             ∃∃K1. ⦃G, L1⦄ ⊢ ➡[h, g] K1 & |K1| = |K2| &
+                   (∀T,d. L1 ⋕[T, d] L2 ↔ K1 ⋕[T, d] K2).
+#h #g #G #L2 #K2 #H elim H -L2 -K2
+[ #L1 #H >(length_inv_zero_dx … H) -L1 /3 width=5 by ex3_intro, conj/
+| #I2 #L2 #K2 #V2 #W2 #_ #HVW2 #IHLK2 #Y #H
+  elim (length_inv_pos_dx … H) -H #I #L1 #V1 #HL12 #H destruct
+  elim (IHLK2 … HL12) -IHLK2 #K1 #HLK1 #HK12 #IH
+  elim (eq_term_dec V1 V2) #H destruct
+  [ @(ex3_intro … (K1.ⓑ{I}W2)) normalize /2 width=1 by /
+*)
+axiom lleq_lpx_trans: ∀h,g,G,L2,K2. ⦃G, L2⦄ ⊢ ➡[h, g] K2 →
+                      ∀L1,T,d. L1 ⋕[T, d] L2 →
+                      ∃∃K1. ⦃G, L1⦄ ⊢ ➡[h, g] K1 & K1 ⋕[T, d] K2.
+(*
+#h #g #G #L2 #K2 #H elim H -L2 -K2
+[ #L1 #T #d #H lapply (lleq_fwd_length … H) -H
+  #H >(length_inv_zero_dx … H) -L1 /2 width=3 by ex2_intro/
+| #I2 #L2 #K2 #V2 #W2 #HLK2 #HVW2 #IHLK2 #Y #T #d #HT
+  lapply (lleq_fwd_length … HT) #H
+  elim (length_inv_pos_dx … H) -H #I1 #L1 #V1 #HL12 #H destruct
+  elim (eq_term_dec V1 V2) #H destruct
+  [ @ex2_intro …
+*)
 
 lemma lpx_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
-                          ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[0, T1] L1 →
-                          ∃∃K2. ⦃G1, K1, T1⦄ ⊃ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[0, T2] L2.
+                          ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
+                          ∃∃K2. ⦃G1, K1, T1⦄ ⊃ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[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 (lpx_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
+  #I1 #K1 #H #H2KL1 lapply (ldrop_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)
@@ -35,8 +74,8 @@ lemma lpx_lleq_fqu_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2,
 qed-.
 
 lemma lpx_lleq_fquq_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
-                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[0, T1] L1 →
-                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[0, T2] L2.
+                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
+                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[T2, 0] L2.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
 elim (fquq_inv_gen … H) -H
 [ #H elim (lpx_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
@@ -46,8 +85,8 @@ elim (fquq_inv_gen … H) -H
 qed-.
 
 lemma lpx_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
-                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[0, T1] L1 →
-                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[0, T2] L2.
+                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
+                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[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 (lpx_lleq_fqu_trans … H … H1KL1 H2KL1) -L1
   /3 width=4 by fqu_fqup, ex3_intro/
@@ -58,8 +97,8 @@ lemma lpx_lleq_fqup_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2
 qed-.
 
 lemma lpx_lleq_fqus_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
-                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[0, T1] L1 →
-                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[0, T2] L2.
+                           ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, g] L1 → K1 ⋕[T1, 0] L1 →
+                           ∃∃K2. ⦃G1, K1, T1⦄ ⊃* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, g] L2 & K2 ⋕[T2, 0] L2.
 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #H1KL1 #H2KL1
 elim (fqus_inv_gen … H) -H
 [ #H elim (lpx_lleq_fqup_trans … H … H1KL1 H2KL1) -L1