Imported Upstream version 8.0pl1upstream/8.0pl1

1 files changed, 31 insertions, 0 deletions

diff --git a/theories/Bool/DecBool.v b/theories/Bool/DecBool.v
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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        *)
+(************************************************************************)
+
+(*i $Id: DecBool.v,v 1.6.2.1 2004/07/16 19:31:03 herbelin Exp $ i*)
+
+Set Implicit Arguments.
+
+Definition ifdec (A B:Prop) (C:Set) (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.
+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.
+intros; case H; auto.
+intro; absurd A; trivial.
+Qed.
+
+Unset Implicit Arguments.
\ No newline at end of file