matita/matita/contribs/lambdadelta/static_2/syntax/ac.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 "ground_2/lib/arith.ma".
  16
  17 (* APPLICABILITY CONDITION  *************************************************)
  18
  19 (* applicability condition specification *)
  20 record ac: Type[0] ≝ {
  21 (* degree of the sort *)
  22    appl: predicate nat
  23 }.
  24
  25 (* applicability condition postulates *)
  26 record ac_props (a): Prop ≝ {
  27    ac_dec: ∀m. Decidable (∃∃n. m ≤ n & appl a n)
  28 }.
  29
  30 (* Notable specifications ***************************************************)
  31
  32 definition apply_top: predicate nat ≝ λn. ⊤.
  33
  34 definition ac_top: ac ≝ mk_ac apply_top.
  35
  36 lemma ac_top_props: ac_props ac_top ≝ mk_ac_props ….
  37 /3 width=3 by or_introl, ex2_intro/
  38 qed.
  39
  40 definition ac_eq (k): ac ≝ mk_ac (eq … k).
  41
  42 lemma ac_eq_props (k): ac_props (ac_eq k) ≝ mk_ac_props ….
  43 #m elim (le_dec m k) #Hm
  44 [ /3 width=3 by or_introl, ex2_intro/
  45 | @or_intror * #n #Hmn #H destruct /2 width=1 by/
  46 ]
  47 qed.