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[helm.git] / helm / software / matita / contribs / procedural / Coq / Arith / Compare.mma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "Coq.ma".
+
+(*#**********************************************************************)
+
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
+
+(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
+
+(*   \VV/  *************************************************************)
+
+(*    //   *      This file is distributed under the terms of the      *)
+
+(*         *       GNU Lesser General Public License Version 2.1       *)
+
+(*#**********************************************************************)
+
+(*i $Id: Compare.v,v 1.12 2004/03/03 15:53:40 marche Exp $ i*)
+
+(*#* Equality is decidable on [nat] *)
+
+(* UNEXPORTED
+Open Local Scope nat_scope.
+*)
+
+(*
+Lemma not_eq_sym : (A:Set)(p,q:A)(~p=q) -> ~(q=p).
+Proof sym_not_eq.
+Hints Immediate not_eq_sym : arith.
+*)
+
+(* NOTATION
+Notation not_eq_sym := sym_not_eq.
+*)
+
+(* UNEXPORTED
+Implicit Types m n p q : nat.
+*)
+
+include "Arith/Arith.ma".
+
+include "Arith/Peano_dec.ma".
+
+include "Arith/Compare_dec.ma".
+
+inline procedural "cic:/Coq/Arith/Compare/le_or_le_S.con" as definition.
+
+inline procedural "cic:/Coq/Arith/Compare/Pcompare.con" as definition.
+
+inline procedural "cic:/Coq/Arith/Compare/le_dec.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Compare/lt_or_eq.con" as definition.
+
+inline procedural "cic:/Coq/Arith/Compare/le_decide.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Compare/le_le_S_eq.con" as lemma.
+
+(* By special request of G. Kahn - Used in Group Theory *)
+
+inline procedural "cic:/Coq/Arith/Compare/discrete_nat.con" as lemma.
+
+include "Arith/Wf_nat.ma".
+
+include "Arith/Min.ma".
+