matita/matita/contribs/lambdadelta/static_2/syntax/tweq_teqx.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/teqx.ma".
  16 include "static_2/syntax/tweq.ma".
  17
  18 (* SORT-IRRELEVANT WHD EQUIVALENCE ON TERMS *********************************)
  19
  20 (* Properties with sort-irrelevant equivalence for terms ********************)
  21
  22 lemma teqx_tweq: ∀T1,T2. T1 ≛ T2 → T1 ≅ T2.
  23 #T1 #T2 #H elim H -T1 -T2 [||| * [ #p ] * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT ]
  24 [ /1 width=1 by tweq_sort/
  25 | /1 width=1 by tweq_lref/
  26 | /1 width=1 by tweq_gref/
  27 | cases p -p /2 width=1 by tweq_abbr_pos, tweq_abbr_neg/
  28 | /1 width=1 by tweq_abst/
  29 | /2 width=1 by tweq_appl/
  30 | /2 width=1 by tweq_cast/
  31 ]
  32 qed.