update for the article

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / feqx.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/notation/relations/stareqsn_6.ma".
+include "static_2/syntax/genv.ma".
+include "static_2/static/reqx.ma".
+
+(* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
+
+inductive feqx (G) (L1) (T1): relation3 genv lenv term ≝
+| feqx_intro_sn: ∀L2,T2. L1 ≛[T1] L2 → T1 ≛ T2 →
+                 feqx G L1 T1 G L2 T2
+.
+
+interpretation
+   "sort-irrelevant equivalence on referred entries (closure)"
+   'StarEqSn G1 L1 T1 G2 L2 T2 = (feqx G1 L1 T1 G2 L2 T2).
+
+(* Basic_properties *********************************************************)
+
+lemma feqx_intro_dx (G): ∀L1,L2,T2. L1 ≛[T2] L2 →
+                         ∀T1. T1 ≛ T2 → ⦃G,L1,T1⦄ ≛ ⦃G,L2,T2⦄.
+/3 width=3 by feqx_intro_sn, teqx_reqx_div/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma feqx_inv_gen_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄ →
+                       ∧∧ G1 = G2 & L1 ≛[T1] L2 & T1 ≛ T2.
+#G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
+qed-.
+
+lemma feqx_inv_gen_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄ →
+                       ∧∧ G1 = G2 & L1 ≛[T2] L2 & T1 ≛ T2.
+#G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/3 width=3 by teqx_reqx_conf, and3_intro/
+qed-.
+
+(* Basic_2A1: removed theorems 6:
+              fleq_refl fleq_sym fleq_inv_gen
+              fleq_trans fleq_canc_sn fleq_canc_dx
+*)