- commit of the "substitution" component

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
index 4b0257e6f453b6bf707fa8271278761e63482bab..d810ae1759c9ccf2e184b8ccb27f9d02fd4b331b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lleq_lleq.ma".
+include "basic_2/substitution/lleq_ext.ma".
 include "basic_2/reduction/cpx.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
@@ -20,10 +20,12 @@ include "basic_2/reduction/cpx.ma".
 (* Properties on lazy equivalence for local environments ********************)
 
 lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
-                      ∀L1. L1 ⋕[0, T1] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
+                      ∀L1. L1 ⋕[T1, 0] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
 #h #g #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2 /2 width=2 by cpx_sort/
-[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_inv_lref_ge_dx … H … HLK2) -L2
-  /3 width=7 by cpx_delta/
+[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_fwd_lref_dx … H … HLK2) -L2
+  [ #H elim (ylt_yle_false … H) //
+  | * /3 width=7 by cpx_delta/
+  ]
 | #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_bind_O … H) -H
   /3 width=1 by cpx_bind/
 | #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
@@ -40,3 +42,33 @@ lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
   #HV1 #H elim (lleq_inv_bind_O … H) -H /3 width=3 by cpx_theta/
 ]
 qed-.
+
+(* Note: lemma 1000 *)
+lemma lleq_cpx_conf_dx: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
+                        ∀L1. L1 ⋕[T1, 0] L2 → L1 ⋕[T2, 0] L2.
+#h #g #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2
+[ //
+| /3 width=3 by lleq_fwd_length, lleq_sort/
+| #I2 #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_inv_lref_ge_dx … H … HLK2) // -H
+  #I1 #K1 #HLK1 #HV1
+  lapply (ldrop_fwd_drop2 … HLK1) -HLK1 #HLK1
+  lapply (ldrop_fwd_drop2 … HLK2) -HLK2 #HLK2
+  @(lleq_lift_le … HLK1 HLK2 … HVW2) -HLK1 -HLK2 -HVW2 /2 width=1 by/ (**) (* full auto too slow *)
+| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_bind_O … H) -H
+  /4 width=5 by lleq_bind_repl_SO, lleq_bind/
+| #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
+  /3 width=1 by lleq_flat/
+| #G #L2 #V #T1 #T2 #T #_ #HT2 #IHT12 #L1 #H elim (lleq_inv_bind_O … H) -H
+  /3 width=10 by lleq_inv_lift_le, ldrop_drop/
+| #G #L2 #V #T1 #T2 #_ #IHT12 #L1 #H elim (lleq_inv_flat … H) -H /2 width=1 by/
+| #G #L2 #V1 #V2 #T #_ #IHV12 #L1 #H elim (lleq_inv_flat … H) -H /2 width=1 by/
+| #a #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
+  #HV1 #H elim (lleq_inv_bind_O … H) -H
+  /4 width=5 by lleq_bind_repl_SO, lleq_flat, lleq_bind/
+| #a #G #L2 #V1 #V2 #V #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
+  #HV1 #H elim (lleq_inv_bind_O … H) -H
+  #HW1 #HT1 @lleq_bind_O /2 width=1 by/ @lleq_flat (**) (* full auto too slow *)
+  [ /3 width=10 by lleq_lift_le, ldrop_drop/
+  | /3 width=3 by lleq_bind_repl_O/
+]
+qed-.