matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper.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 "delayed_updating/syntax/prototerm.ma".
  16 include "delayed_updating/syntax/path_proper.ma".
  17 include "ground/lib/subset_ext_equivalence.ma".
  18
  19 (* PROPER CONDITION FOR PROTOTERM *******************************************)
  20
  21 interpretation
  22   "proper condition (prototerm)"
  23   'ClassP = (subset_ext_p1 path ppc).
  24
  25 (* Basic constructions ******************************************************)
  26
  27 lemma tpc_i (t):
  28       (𝐞 ⧸ϵ t) → t ϵ 𝐏.
  29 #t #Ht * //
  30 #H elim (Ht H)
  31 qed.
  32
  33 (* Basic inversions *********************************************************)
  34
  35 lemma in_ppc_comp_trans (t) (p):
  36       p ϵ t → t ϵ 𝐏 → p ϵ 𝐏.
  37 #t #p #Hp #Ht
  38 @(Ht … Hp)
  39 qed-.
  40
  41 lemma tpc_e (t): 𝐞 ϵ t → t ϵ 𝐏 → ⊥.
  42 /2 width=5 by in_ppc_comp_trans/ qed-.