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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Local Open Scope nat_scope.
Definition zerob (n:nat) : bool :=
match n with
| O => true
| S _ => false
end.
Hint Resolve zerob_true_intro: bool.
Hint Resolve zerob_false_intro: bool.

Lemma zerob_false_elim : forall n:nat, zerob n = false -> n <> 0.