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(* $Id$ *)
Implicit Arguments On.
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.
Save.
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.
Save.
Implicit Arguments Off.
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