Library Coq.Bool.DecBool
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.
Theorem ifdec_right :
forall (A B:Prop) (C:Set) (H:{A} + {B}),
~ A -> forall x y:C, ifdec H x y = y.
Unset Implicit Arguments.