Definition ifdec (A B:Prop) (C:Type) (H:{A} + {B}) (x y:C) : C :=
  if H then x else y.

(* Specifications: *)
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.