matita/matita/contribs/lambdadelta/static_2/static/reqg_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_teqg.ma".
  16 include "static_2/static/rex_drops.ma".
  17 include "static_2/static/reqg.ma".
  18
  19 (* GENERIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***********)
  20
  21 (* Properties with generic slicing for local environments *******************)
  22
  23 lemma reqg_lifts_sn (S):
  24       reflexive … S → f_dedropable_sn (ceqg S).
  25 /3 width=5 by rex_liftable_dedropable_sn, teqg_lifts_sn, teqg_refl/ qed-.
  26
  27 (* Inversion lemmas with generic slicing for local environments *************)
  28
  29 lemma reqg_inv_lifts_sn (S):
  30       f_dropable_sn (ceqg S).
  31 /2 width=5 by rex_dropable_sn/ qed-.
  32
  33 lemma reqg_inv_lifts_dx (S):
  34       f_dropable_dx (ceqg S).
  35 /2 width=5 by rex_dropable_dx/ qed-.
  36
  37 lemma reqg_inv_lifts_bi (S):
  38       ∀L1,L2,U. L1 ≛[S,U] L2 → ∀b,f. 𝐔❨f❩ →
  39       ∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
  40       ∀T. ⇧*[f] T ≘ U → K1 ≛[S,T] K2.
  41 /2 width=10 by rex_inv_lifts_bi/ qed-.
  42
  43 lemma reqg_inv_lref_pair_sn (S):
  44       ∀L1,L2,i. L1 ≛[S,#i] L2 → ∀I,K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I]V1 →
  45       ∃∃K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I]V2 & K1 ≛[S,V1] K2 & V1 ≛[S] V2.
  46 /2 width=3 by rex_inv_lref_pair_sn/ qed-.
  47
  48 lemma reqg_inv_lref_pair_dx (S):
  49       ∀L1,L2,i. L1 ≛[S,#i] L2 → ∀I,K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I]V2 →
  50       ∃∃K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I]V1 & K1 ≛[S,V1] K2 & V1 ≛[S] V2.
  51 /2 width=3 by rex_inv_lref_pair_dx/ qed-.
  52
  53 lemma reqg_inv_lref_pair_bi (S) (L1) (L2) (i):
  54       L1 ≛[S,#i] L2 →
  55       ∀I1,K1,V1. ⇩[i] L1 ≘ K1.ⓑ[I1]V1 →
  56       ∀I2,K2,V2. ⇩[i] L2 ≘ K2.ⓑ[I2]V2 →
  57       ∧∧ K1 ≛[S,V1] K2 & V1 ≛[S] V2 & I1 = I2.
  58 /2 width=6 by rex_inv_lref_pair_bi/ qed-.