helm/software/matita/contribs/procedural/Coq/Arith/Compare_dec.mma

   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 (* This file was automatically generated: do not edit *********************)
  16
  17 include "Coq.ma".
  18
  19 (*#***********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  22
  23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  24
  25 (*   \VV/  **************************************************************)
  26
  27 (*    //   *      This file is distributed under the terms of the       *)
  28
  29 (*         *       GNU Lesser General Public License Version 2.1        *)
  30
  31 (*#***********************************************************************)
  32
  33 (*i $Id: Compare_dec.v,v 1.13.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 include "Arith/Le.ma".
  36
  37 include "Arith/Lt.ma".
  38
  39 include "Arith/Gt.ma".
  40
  41 include "Logic/Decidable.ma".
  42
  43 (* UNEXPORTED
  44 Open Local Scope nat_scope.
  45 *)
  46
  47 (* UNEXPORTED
  48 Implicit Types m n x y : nat.
  49 *)
  50
  51 inline procedural "cic:/Coq/Arith/Compare_dec/zerop.con" as definition.
  52
  53 inline procedural "cic:/Coq/Arith/Compare_dec/lt_eq_lt_dec.con" as definition.
  54
  55 inline procedural "cic:/Coq/Arith/Compare_dec/gt_eq_gt_dec.con" as lemma.
  56
  57 inline procedural "cic:/Coq/Arith/Compare_dec/le_lt_dec.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Arith/Compare_dec/le_le_S_dec.con" as definition.
  60
  61 inline procedural "cic:/Coq/Arith/Compare_dec/le_ge_dec.con" as definition.
  62
  63 inline procedural "cic:/Coq/Arith/Compare_dec/le_gt_dec.con" as definition.
  64
  65 inline procedural "cic:/Coq/Arith/Compare_dec/le_lt_eq_dec.con" as definition.
  66
  67 (*#* Proofs of decidability *)
  68
  69 inline procedural "cic:/Coq/Arith/Compare_dec/dec_le.con" as theorem.
  70
  71 inline procedural "cic:/Coq/Arith/Compare_dec/dec_lt.con" as theorem.
  72
  73 inline procedural "cic:/Coq/Arith/Compare_dec/dec_gt.con" as theorem.
  74
  75 inline procedural "cic:/Coq/Arith/Compare_dec/dec_ge.con" as theorem.
  76
  77 inline procedural "cic:/Coq/Arith/Compare_dec/not_eq.con" as theorem.
  78
  79 inline procedural "cic:/Coq/Arith/Compare_dec/not_le.con" as theorem.
  80
  81 inline procedural "cic:/Coq/Arith/Compare_dec/not_gt.con" as theorem.
  82
  83 inline procedural "cic:/Coq/Arith/Compare_dec/not_ge.con" as theorem.
  84
  85 inline procedural "cic:/Coq/Arith/Compare_dec/not_lt.con" as theorem.
  86