matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_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 "basic_2/relocation/lifts_tdeq.ma".
  16 include "basic_2/static/lfxs_drops.ma".
  17 include "basic_2/static/lfdeq.ma".
  18
  19 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
  20
  21 (* Properties with generic slicing for local environments *******************)
  22
  23 (* Basic_2A1: includes: lleq_lift_le lleq_lift_ge *)
  24 lemma lfdeq_lifts_sn: ∀h,o. dedropable_sn (cdeq h o).
  25 /3 width=5 by lfxs_liftable_dedropable_sn, tdeq_lifts_sn/ qed-.
  26
  27 (* Inversion lemmas with generic slicing for local environments *************)
  28
  29 (* Basic_2A1: restricts: lleq_inv_lift_le lleq_inv_lift_be lleq_inv_lift_ge *)
  30 lemma lfdeq_inv_lifts_sn: ∀h,o. dropable_sn (cdeq h o).
  31 /2 width=5 by lfxs_dropable_sn/ qed-.
  32
  33 (* Note: missing in basic_2A1 *)
  34 lemma lfdeq_inv_lifts_dx: ∀h,o. dropable_dx (cdeq h o).
  35 /2 width=5 by lfxs_dropable_dx/ qed-.
  36
  37 (* Note: missing in basic_2A1 *)
  38 lemma lfdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≡[h, o, U] L2 →
  39                           ∀K1,K2,i. ⬇*[i] L1 ≡ K1 → ⬇*[i] L2 ≡ K2 →
  40                           ∀T. ⬆*[i] T ≡ U → K1 ≡[h, o, T] K2.
  41 /2 width=8 by lfxs_inv_lifts_bi/ qed-.
  42
  43 lemma lfdeq_inv_lref_pair_sn: ∀h,o,L1,L2,i. L1 ≡[h, o, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 →
  44                               ∃∃K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 & K1 ≡[h, o, V1] K2 & V1 ≡[h, o] V2.
  45 /2 width=3 by lfxs_inv_lref_pair_sn/ qed-.
  46
  47 lemma lfdeq_inv_lref_pair_dx: ∀h,o,L1,L2,i. L1 ≡[h, o, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 →
  48                               ∃∃K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 & K1 ≡[h, o, V1] K2 & V1 ≡[h, o] V2.
  49 /2 width=3 by lfxs_inv_lref_pair_dx/ qed-.