X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fequivalence%2Flsubse_ldrop.ma;fp=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fequivalence%2Flsubse_ldrop.ma;h=729f4b61fb0ed6825acd3ff7e5ec6c7bd97bdc27;hb=4bea40e6589ce21c15ecf99bdd5bd2a1c62f6809;hp=0000000000000000000000000000000000000000;hpb=943bfd67310c34c05cbba627272864eb10800143;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/equivalence/lsubse_ldrop.ma b/matita/matita/contribs/lambda_delta/basic_2/equivalence/lsubse_ldrop.ma
new file mode 100644
index 000000000..729f4b61f
--- /dev/null
+++ b/matita/matita/contribs/lambda_delta/basic_2/equivalence/lsubse_ldrop.ma
@@ -0,0 +1,65 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/equivalence/lsubse.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR CONTEXT-SENSITIVE PARALLEL EQUIVALENCE **)
+
+(* Properties concerning basic local environment slicing ********************)
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsubse_ldrop_O1_conf: ∀h,g,L1,L2. h ⊢ L1 ⊢•⊑[g] L2 →
+                            ∀K1,e. ⇩[0, e] L1 ≡ K1 →
+                            ∃∃K2. h ⊢ K1 ⊢•⊑[g] K2 & ⇩[0, e] L2 ≡ K2.
+#h #g #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3/
+| #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
+  elim (ldrop_inv_O1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
+  | elim (IHL12 … HLK1) -L1 /3 width=3/
+  ]
+| #L1 #L2 #V1 #V2 #W1 #W2 #l #HW12 #HVW1 #HWV2 #_ #IHL12 #K1 #e #H
+  elim (ldrop_inv_O1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_refl … H) in HL12; -H /3 width=6/
+  | elim (IHL12 … HLK1) -L1 /3 width=3/
+  ]
+]
+qed-.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsubse_ldrop_O1_trans: ∀h,g,L1,L2. h ⊢ L1 ⊢•⊑[g] L2 →
+                             ∀K2,e. ⇩[0, e] L2 ≡ K2 →
+                             ∃∃K1. h ⊢ K1 ⊢•⊑[g] K2 & ⇩[0, e] L1 ≡ K1.
+#h #g #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3/
+| #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
+  elim (ldrop_inv_O1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
+  | elim (IHL12 … HLK2) -L2 /3 width=3/
+  ]
+| #L1 #L2 #V1 #V2 #W1 #W2 #l #HW12 #HVW1 #HWV2 #_ #IHL12 #K2 #e #H
+  elim (ldrop_inv_O1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_refl … H) in HL12; -H /3 width=6/
+  | elim (IHL12 … HLK2) -L2 /3 width=3/
+  ]
+]
+qed-.