milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / lsubn / lsubn_ldrop.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/lsubn/lsubn_ldrop.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/lsubn/lsubn_ldrop.etc
new file mode 100644 (file)
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--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/lsubn/lsubn_ldrop.etc
@@ -0,0 +1,64 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/dynamic/lsubn.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
+
+(* Properties concerning basic local environment slicing ********************)
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsubn_ldrop_O1_conf: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀K1,e. ⇩[0, e] L1 ≡ K1 →
+                           ∃∃K2. h ⊢ K1 :⊑ K2 & ⇩[0, e] L2 ≡ K2.
+#h #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 #V #W #H1VW #H2VW #_ #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/
+  ]
+]
+qed.
+
+(* Note: the constant 0 cannot be generalized *)
+(* Basic_1: was only: csubt_drop_abbr csubt_drop_abst *)
+lemma lsubn_ldrop_O1_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
+                            ∃∃K1. h ⊢ K1 :⊑ K2 & ⇩[0, e] L1 ≡ K1.
+#h #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 #V #W #H1VW #H2VW #_ #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/
+  ]
+]
+qed.