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(***********************************************************************)
(* 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 *)
(***********************************************************************)
Require Decidable.
(* $Id$ *)
Theorem O_or_S : (n:nat)({m:nat|(S m)=n})+{O=n}.
Proof.
Induction n.
Auto.
Intros p H; Left; Exists p; Auto.
Qed.
Theorem eq_nat_dec : (n,m:nat){n=m}+{~(n=m)}.
Proof.
Induction n; Induction m; Auto.
Intros q H'; Elim (H q); Auto.
Qed.
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.
Save.
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