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-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(*i $Id: Peano_dec.v,v 1.1.2.1 2004/07/16 19:31:25 herbelin Exp $ i*)
-
-Require Decidable.
-
-V7only [Import nat_scope.].
-Open Local Scope nat_scope.
-
-Implicit Variables Type m,n,x,y:nat.
-
-Theorem O_or_S : (n:nat)({m:nat|(S m)=n})+{O=n}.
-Proof.
-NewInduction n.
-Auto.
-Left; Exists n; Auto.
-Defined.
-
-Theorem eq_nat_dec : (n,m:nat){n=m}+{~(n=m)}.
-Proof.
-NewInduction n; NewInduction m; Auto.
-Elim (IHn m); Auto.
-Defined.
-
-Hints Resolve O_or_S eq_nat_dec : arith.
-
-Theorem dec_eq_nat:(x,y:nat)(decidable (x=y)).
-Intros x y; Unfold decidable; Elim (eq_nat_dec x y); Auto with arith.
-Defined.
-