renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / rdeq_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/rdeq_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/rdeq_drops.ma
new file mode 100644 (file)
index 0000000..1cff3b9
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/rdeq_drops.ma
@@ -0,0 +1,47 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/lifts_tdeq.ma".
+include "basic_2/static/rex_drops.ma".
+include "basic_2/static/rdeq.ma".
+
+(* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
+
+(* Properties with generic slicing for local environments *******************)
+
+lemma rdeq_lifts_sn: ∀h,o. f_dedropable_sn (cdeq h o).
+/3 width=5 by rex_liftable_dedropable_sn, tdeq_lifts_sn/ qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+lemma rdeq_inv_lifts_sn: ∀h,o. f_dropable_sn (cdeq h o).
+/2 width=5 by rex_dropable_sn/ qed-.
+
+(* Note: missing in basic_2A1 *)
+lemma rdeq_inv_lifts_dx: ∀h,o. f_dropable_dx (cdeq h o).
+/2 width=5 by rex_dropable_dx/ qed-.
+
+(* Basic_2A1: uses: lleq_inv_lift_le lleq_inv_lift_be lleq_inv_lift_ge *)
+lemma rdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≛[h, o, U] L2 → ∀b,f. 𝐔⦃f⦄ →
+                         ∀K1,K2. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
+                         ∀T. ⬆*[f] T ≘ U → K1 ≛[h, o, T] K2.
+/2 width=10 by rex_inv_lifts_bi/ qed-.
+
+lemma rdeq_inv_lref_pair_sn: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
+                             ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
+/2 width=3 by rex_inv_lref_pair_sn/ qed-.
+
+lemma rdeq_inv_lref_pair_dx: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
+                             ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
+/2 width=3 by rex_inv_lref_pair_dx/ qed-.