+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/lsubr.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR SUBSTITUTION ****************************)
-
-(* Auxiliary inversion lemmas ***********************************************)
-
-fact lsubr_inv_abbr1_aux: ∀L1,L2. L1 ⊑ L2 → ∀K1,W. L1 = K1.ⓓW →
- ∨∨ L2 = ⋆
- | ∃∃K2. K1 ⊑ K2 & L2 = K2.ⓓW
- | ∃∃K2,W2. K1 ⊑ K2 & L2 = K2.ⓛW2.
-#L1 #L2 * -L1 -L2
-[ #L #K1 #W #H destruct /2 width=1/
-| #L1 #L2 #V #HL12 #K1 #W #H destruct /3 width=3/
-| #I #L1 #L2 #V1 #V2 #HL12 #K1 #W #H destruct /3 width=4/
-]
-qed-.
-
-lemma lsubr_inv_abbr1: ∀K1,L2,W. K1.ⓓW ⊑ L2 →
- ∨∨ L2 = ⋆
- | ∃∃K2. K1 ⊑ K2 & L2 = K2.ⓓW
- | ∃∃K2,W2. K1 ⊑ K2 & L2 = K2.ⓛW2.
-/2 width=3 by lsubr_inv_abbr1_aux/ qed-.
-
-fact lsubr_inv_abst1_aux: ∀L1,L2. L1 ⊑ L2 → ∀K1,W1. L1 = K1.ⓛW1 →
- L2 = ⋆ ∨
- ∃∃K2,W2. K1 ⊑ K2 & L2 = K2.ⓛW2.
-#L1 #L2 * -L1 -L2
-[ #L #K1 #W1 #H destruct /2 width=1/
-| #L1 #L2 #V #_ #K1 #W1 #H destruct
-| #I #L1 #L2 #V1 #V2 #HL12 #K1 #W1 #H destruct /3 width=4/
-]
-qed-.
-
-lemma lsubr_inv_abst1: ∀K1,L2,W1. K1.ⓛW1 ⊑ L2 →
- L2 = ⋆ ∨
- ∃∃K2,W2. K1 ⊑ K2 & L2 = K2.ⓛW2.
-/2 width=4 by lsubr_inv_abst1_aux/ qed-.
-
-(* Main properties **********************************************************)
-
-theorem lsubr_trans: Transitive … lsubr.
-#L1 #L #H elim H -L1 -L
-[ #L1 #X #H
- lapply (lsubr_inv_atom1 … H) -H //
-| #L1 #L #V #_ #IHL1 #X #H
- elim (lsubr_inv_abbr1 … H) -H // *
- #L2 [2: #V2 ] #HL2 #H destruct /3 width=1/
-| #I #L1 #L #V1 #V #_ #IHL1 #X #H
- elim (lsubr_inv_abst1 … H) -H // *
- #L2 #V2 #HL2 #H destruct /3 width=1/
-]
-qed-.