matita/matita/contribs/lambdadelta/static_2/static/reqg_fqup.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/static/rex_fqup.ma".
  16 include "static_2/static/reqg.ma".
  17
  18 (* GEBERIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***********)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma reqg_refl (S):
  23       reflexive … S →
  24       c_reflexive … (reqg S).
  25 /3 width=1 by rex_refl, teqg_refl/ qed.
  26
  27 lemma reqg_pair_refl (S):
  28       reflexive … S →
  29       ∀V1,V2. V1 ≛[S] V2 →
  30       ∀I,L. ∀T:term. L.ⓑ[I]V1 ≛[S,T] L.ⓑ[I]V2.
  31 /3 width=1 by rex_pair_refl, teqg_refl/ qed.
  32
  33 (* Advanced inversion lemmas ************************************************)
  34
  35 lemma reqg_inv_bind_void (S):
  36       ∀p,I,L1,L2,V,T. L1 ≛[S,ⓑ[p,I]V.T] L2 →
  37       ∧∧ L1 ≛[S,V] L2 & L1.ⓧ ≛[S,T] L2.ⓧ.
  38 /2 width=3 by rex_inv_bind_void/ qed-.
  39
  40 (* Advanced forward lemmas **************************************************)
  41
  42 lemma reqg_fwd_bind_dx_void (S):
  43       ∀p,I,L1,L2,V,T.
  44       L1 ≛[S,ⓑ[p,I]V.T] L2 → L1.ⓧ ≛[S,T] L2.ⓧ.
  45 /2 width=4 by rex_fwd_bind_dx_void/ qed-.