matita/matita/contribs/lambdadelta/static_2/syntax/teqw_teqg.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/syntax/teqg.ma".
  16 include "static_2/syntax/teqw.ma".
  17
  18 (* SORT-IRRELEVANT WHD EQUIVALENCE ON TERMS *********************************)
  19
  20 (* Properties with generic equivalence for terms ****************************)
  21
  22 lemma teqg_teqw (S):
  23       ∀T1,T2. T1 ≛[S] T2 → T1 ≃ T2.
  24 #S #T1 #T2 #H elim H -T1 -T2 [||| * [ #p ] * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT ]
  25 [ /1 width=1 by teqw_sort/
  26 | /1 width=1 by teqw_lref/
  27 | /1 width=1 by teqw_gref/
  28 | cases p -p /2 width=1 by teqw_abbr_pos, teqw_abbr_neg/
  29 | /1 width=1 by teqw_abst/
  30 | /2 width=1 by teqw_appl/
  31 | /2 width=1 by teqw_cast/
  32 ]
  33 qed.