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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
Set Implicit Arguments.
Definition ifdec (A B:Prop) (C:Type) (H:{A} + {B}) (x y:C) : C :=
if H then x else y.
Theorem ifdec_left :
forall (A B:Prop) (C:Set) (H:{A} + {B}),
~ B -> forall x y:C, ifdec H x y = x.
Proof.
intros; case H; auto.
intro; absurd B; trivial.
Qed.
Theorem ifdec_right :
forall (A B:Prop) (C:Set) (H:{A} + {B}),
~ A -> forall x y:C, ifdec H x y = y.
Proof.
intros; case H; auto.
intro; absurd A; trivial.
Qed.
Unset Implicit Arguments.
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