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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        *)
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(*i $Id: DecBool.v,v 1.1.2.1 2004/07/16 19:31:25 herbelin Exp $ i*)

Set Implicit Arguments.

Definition ifdec : (A,B:Prop)(C:Set)({A}+{B})->C->C->C
   := [A,B,C,H,x,y]if H then [_]x else [_]y.


Theorem ifdec_left : (A,B:Prop)(C:Set)(H:{A}+{B})~B->(x,y:C)(ifdec H x y)=x.
Intros; Case H; Auto.
Intro; Absurd B; Trivial.
Qed.

Theorem ifdec_right : (A,B:Prop)(C:Set)(H:{A}+{B})~A->(x,y:C)(ifdec H x y)=y.
Intros; Case H; Auto.
Intro; Absurd A; Trivial.
Qed.

Unset Implicit Arguments.