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 (* Note: missing in basic_2A1 *)
  32 lemma rdeq_inv_lifts_dx: ∀h,o. f_dropable_dx (cdeq h o).
  33 /2 width=5 by rex_dropable_dx/ qed-.
  34
  35 (* Basic_2A1: uses: lleq_inv_lift_le lleq_inv_lift_be lleq_inv_lift_ge *)
  36 lemma rdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≛[h, o, U] L2 → ∀b,f. 𝐔⦃f⦄ →
  37                          ∀K1,K2. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
  38                          ∀T. ⬆*[f] T ≘ U → K1 ≛[h, o, T] K2.
  39 /2 width=10 by rex_inv_lifts_bi/ qed-.
  40
  41 lemma rdeq_inv_lref_pair_sn: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
  42                              ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
  43 /2 width=3 by rex_inv_lref_pair_sn/ qed-.
  44
  45 lemma rdeq_inv_lref_pair_dx: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
  46                              ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
  47 /2 width=3 by rex_inv_lref_pair_dx/ qed-.