syntactic components detached from basic_2 become static_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fdeq.ma b/matita/matita/contribs/lambdadelta/static_2/static/fdeq.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_8.ma".
+include "static_2/syntax/genv.ma".
+include "static_2/static/rdeq.ma".
+
+(* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
+
+inductive fdeq (h) (o) (G) (L1) (T1): relation3 genv lenv term ≝
+| fdeq_intro_sn: ∀L2,T2. L1 ≛[h, o, T1] L2 → T1 ≛[h, o] T2 →
+                 fdeq h o G L1 T1 G L2 T2
+.
+
+interpretation
+   "degree-based equivalence on referred entries (closure)"
+   'StarEqSn h o G1 L1 T1 G2 L2 T2 = (fdeq h o G1 L1 T1 G2 L2 T2).
+
+(* Basic_properties *********************************************************)
+
+lemma fdeq_intro_dx (h) (o) (G): ∀L1,L2,T2. L1 ≛[h, o, T2] L2 →
+                                 ∀T1. T1 ≛[h, o] T2 → ⦃G, L1, T1⦄ ≛[h, o] ⦃G, L2, T2⦄.
+/3 width=3 by fdeq_intro_sn, tdeq_rdeq_div/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma fdeq_inv_gen_sn: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
+                       ∧∧ G1 = G2 & L1 ≛[h, o, T1] L2 & T1 ≛[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
+qed-.
+
+lemma fdeq_inv_gen_dx: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
+                       ∧∧ G1 = G2 & L1 ≛[h, o, T2] L2 & T1 ≛[h, o] T2.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/3 width=3 by tdeq_rdeq_conf, and3_intro/
+qed-.
+
+(* Basic_2A1: removed theorems 6:
+              fleq_refl fleq_sym fleq_inv_gen
+              fleq_trans fleq_canc_sn fleq_canc_dx
+*)