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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: Zerob.v,v 1.1.2.1 2004/07/16 19:31:25 herbelin Exp $ i*)
-
-Require Arith.
-Require Bool.
-
-V7only [Import nat_scope.].
-Open Local Scope nat_scope.
-
-Definition zerob : nat->bool
- := [n:nat]Cases n of O => true | (S _) => false end.
-
-Lemma zerob_true_intro : (n:nat)(n=O)->(zerob n)=true.
-NewDestruct n; [Trivial with bool | Inversion 1].
-Qed.
-Hints Resolve zerob_true_intro : bool.
-
-Lemma zerob_true_elim : (n:nat)(zerob n)=true->(n=O).
-NewDestruct n; [Trivial with bool | Inversion 1].
-Qed.
-
-Lemma zerob_false_intro : (n:nat)~(n=O)->(zerob n)=false.
-NewDestruct n; [NewDestruct 1; Auto with bool | Trivial with bool].
-Qed.
-Hints Resolve zerob_false_intro : bool.
-
-Lemma zerob_false_elim : (n:nat)(zerob n)=false -> ~(n=O).
-NewDestruct n; [Intro H; Inversion H | Auto with bool].
-Qed.