not : Bool -> Bool.
not = \x. if x then False else True.

t : Bool -> U.
t = \b. if b then Unit else Bool.

bar : (y : Bool) -> t y.
bar = \b. if b then () else True.

x : Unit.
x = bar True.

y : Bool.
y = bar False.

z : (Unit = t True).
z = Refl.

w : (Bool = t False).
w = Refl.
