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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
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33 (*i $Id: Compare.v,v 1.12.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
35 (*#* Equality is decidable on [nat] *)
38 Open Local Scope nat_scope.
42 Lemma not_eq_sym : (A:Set)(p,q:A)(~p=q) -> ~(q=p).
44 Hints Immediate not_eq_sym : arith.
48 Notation not_eq_sym := sym_not_eq.
52 Implicit Types m n p q : nat.
55 include "Arith/Arith.ma".
57 include "Arith/Peano_dec.ma".
59 include "Arith/Compare_dec.ma".
61 inline procedural "cic:/Coq/Arith/Compare/le_or_le_S.con" as definition.
63 inline procedural "cic:/Coq/Arith/Compare/Pcompare.con" as definition.
65 inline procedural "cic:/Coq/Arith/Compare/le_dec.con" as lemma.
67 inline procedural "cic:/Coq/Arith/Compare/lt_or_eq.con" as definition.
69 inline procedural "cic:/Coq/Arith/Compare/le_decide.con" as lemma.
71 inline procedural "cic:/Coq/Arith/Compare/le_le_S_eq.con" as lemma.
73 (* By special request of G. Kahn - Used in Group Theory *)
75 inline procedural "cic:/Coq/Arith/Compare/discrete_nat.con" as lemma.
77 include "Arith/Wf_nat.ma".
79 include "Arith/Min.ma".