(************************************************************************)
(*         *   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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(** Properties of decidable propositions *)
Definition decidable (P:Prop) := P \/ ~ P.

Theorem not_iff :
forall A B:Prop, decidable A -> decidable B ->
~ (A <-> B) -> (A /\ ~ B) \/ (~ A /\ B).