matita/matita/contribs/lambdadelta/static_2/syntax/sh_props.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/sh_nexts.ma".
  16
  17 (* SORT HIERARCHY ***********************************************************)
  18
  19 (* acyclicity condition *)
  20 record sh_acyclic (h): Prop ≝
  21 {
  22 (**) (* use extensional equivalence *)
  23   sh_nexts_inj: ∀s,n1,n2. ⇡*[h,n1]s = ⇡*[h,n2]s → n1 = n2
  24 }.
  25
  26 (* decidability condition *)
  27 record sh_decidable (h): Prop ≝
  28 {
  29   sh_nexts_dec: ∀s1,s2. Decidable (∃n. ⇡*[h,n]s1 = s2)
  30 }.