matita/matita/contribs/lambdadelta/delayed_updating/syntax/term.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/path.ma".
  16 include "delayed_updating/notation/relations/up_down_arrow_epsilon_2.ma".
  17 include "delayed_updating/notation/relations/up_arrow_epsilon_2.ma".
  18
  19 (* TERM *********************************************************************)
  20
  21 definition term: Type[0] ≝ predicate path.
  22
  23 definition term_in_com: relation2 path term ≝
  24            λp,t. t p.
  25
  26 interpretation
  27   "belongs to complete (term)"
  28   'UpDownArrowEpsilon p t = (term_in_com p t).
  29
  30 definition term_in_ini: relation2 path term ≝
  31            λp,t. ∃q. p;;q ϵ⬦ t.
  32
  33 interpretation
  34   "belongs to initial (term)"
  35   'UpArrowEpsilon p t = (term_in_ini p t).
  36
  37 (* Basic constructions ******************************************************)
  38
  39 lemma term_in_com_ini (p) (t):
  40       p ϵ⬦ t → p ϵ▵ t.
  41 /2 width=2 by ex_intro/
  42 qed.