(************************************************************************)
(*         *   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)         *)
(************************************************************************)
Inductive IfProp (A B:Prop) : bool -> Prop :=
| Iftrue : A -> IfProp A B true
| Iffalse : B -> IfProp A B false.
Hint Resolve Iftrue Iffalse: bool.
destruct 1; intros; auto with bool.
case diff_true_false; auto with bool.
Qed.

Lemma Iffalse_inv :
forall (A B:Prop) (b:bool), IfProp A B b -> b = false -> B.