update in static_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqg_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqg_drops.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/relocation/lifts_teqg.ma".
+include "static_2/static/rex_drops.ma".
+include "static_2/static/reqg.ma".
+
+(* GENERIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***********)
+
+(* Properties with generic slicing for local environments *******************)
+
+lemma reqg_lifts_sn (S):
+      reflexive … S → f_dedropable_sn (ceqg S).
+/3 width=5 by rex_liftable_dedropable_sn, teqg_lifts_sn, teqg_refl/ qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+lemma reqg_inv_lifts_sn (S):
+      f_dropable_sn (ceqg S).
+/2 width=5 by rex_dropable_sn/ qed-.
+
+lemma reqg_inv_lifts_dx (S):
+      f_dropable_dx (ceqg S).
+/2 width=5 by rex_dropable_dx/ qed-.
+
+lemma reqg_inv_lifts_bi (S):
+      ∀L1,L2,U. L1 ≛[S,U] L2 → ∀b,f. 𝐔❪f❫ →
+      ∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
+      ∀T. ⇧*[f] T ≘ U → K1 ≛[S,T] K2.
+/2 width=10 by rex_inv_lifts_bi/ qed-.
+
+lemma reqg_inv_lref_pair_sn (S):
+      ∀L1,L2,i. L1 ≛[S,#i] L2 → ∀I,K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I]V1 →
+      ∃∃K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I]V2 & K1 ≛[S,V1] K2 & V1 ≛[S] V2.
+/2 width=3 by rex_inv_lref_pair_sn/ qed-.
+
+lemma reqg_inv_lref_pair_dx (S):
+      ∀L1,L2,i. L1 ≛[S,#i] L2 → ∀I,K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I]V2 →
+      ∃∃K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I]V1 & K1 ≛[S,V1] K2 & V1 ≛[S] V2.
+/2 width=3 by rex_inv_lref_pair_dx/ qed-.
+
+lemma reqg_inv_lref_pair_bi (S) (L1) (L2) (i):
+      L1 ≛[S,#i] L2 →
+      ∀I1,K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I1]V1 →
+      ∀I2,K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I2]V2 →
+      ∧∧ K1 ≛[S,V1] K2 & V1 ≛[S] V2 & I1 = I2.
+/2 width=6 by rex_inv_lref_pair_bi/ qed-.