matita/matita/contribs/lambdadelta/static_2/static/rdeq_drops.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "static_2/relocation/lifts_tdeq.ma".
  16 include "static_2/static/rex_drops.ma".
  17 include "static_2/static/rdeq.ma".
  18
  19 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
  20
  21 (* Properties with generic slicing for local environments *******************)
  22
  23 lemma rdeq_lifts_sn: ∀h,o. f_dedropable_sn (cdeq h o).
  24 /3 width=5 by rex_liftable_dedropable_sn, tdeq_lifts_sn/ qed-.
  25
  26 (* Inversion lemmas with generic slicing for local environments *************)
  27
  28 lemma rdeq_inv_lifts_sn: ∀h,o. f_dropable_sn (cdeq h o).
  29 /2 width=5 by rex_dropable_sn/ qed-.
  30
  31 lemma rdeq_inv_lifts_dx: ∀h,o. f_dropable_dx (cdeq h o).
  32 /2 width=5 by rex_dropable_dx/ qed-.
  33
  34 lemma rdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≛[h, o, U] L2 → ∀b,f. 𝐔⦃f⦄ →
  35                          ∀K1,K2. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
  36                          ∀T. ⬆*[f] T ≘ U → K1 ≛[h, o, T] K2.
  37 /2 width=10 by rex_inv_lifts_bi/ qed-.
  38
  39 lemma rdeq_inv_lref_pair_sn: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
  40                              ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
  41 /2 width=3 by rex_inv_lref_pair_sn/ qed-.
  42
  43 lemma rdeq_inv_lref_pair_dx: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
  44                              ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
  45 /2 width=3 by rex_inv_lref_pair_dx/ qed-.
  46
  47 lemma rdeq_inv_lref_pair_bi (h) (o) (L1) (L2) (i):
  48                             L1 ≛[h,o,#i] L2 →
  49                             ∀I1,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I1}V1 →
  50                             ∀I2,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I2}V2 →
  51                             ∧∧ K1 ≛[h,o,V1] K2 & V1 ≛[h,o] V2 & I1 = I2.
  52 /2 width=6 by rex_inv_lref_pair_bi/ qed-.