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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  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.v,v 1.12.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 (*#* Equality is decidable on [nat] *)
  36
  37 (* UNEXPORTED
  38 Open Local Scope nat_scope.
  39 *)
  40
  41 (*
  42 Lemma not_eq_sym : (A:Set)(p,q:A)(~p=q) -> ~(q=p).
  43 Proof sym_not_eq.
  44 Hints Immediate not_eq_sym : arith.
  45 *)
  46
  47 (* NOTATION
  48 Notation not_eq_sym := sym_not_eq.
  49 *)
  50
  51 (* UNEXPORTED
  52 Implicit Types m n p q : nat.
  53 *)
  54
  55 include "Arith/Arith.ma".
  56
  57 include "Arith/Peano_dec.ma".
  58
  59 include "Arith/Compare_dec.ma".
  60
  61 inline procedural "cic:/Coq/Arith/Compare/le_or_le_S.con" as definition.
  62
  63 inline procedural "cic:/Coq/Arith/Compare/Pcompare.con" as definition.
  64
  65 inline procedural "cic:/Coq/Arith/Compare/le_dec.con" as lemma.
  66
  67 inline procedural "cic:/Coq/Arith/Compare/lt_or_eq.con" as definition.
  68
  69 inline procedural "cic:/Coq/Arith/Compare/le_decide.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Arith/Compare/le_le_S_eq.con" as lemma.
  72
  73 (* By special request of G. Kahn - Used in Group Theory *)
  74
  75 inline procedural "cic:/Coq/Arith/Compare/discrete_nat.con" as lemma.
  76
  77 include "Arith/Wf_nat.ma".
  78
  79 include "Arith/Min.ma".
  80