Coq.Bool.DecBool

# Module Coq.Bool.DecBool

`Set Implicit Arguments.

`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`.

`Unset` Implicit Arguments.

`

Index