#[global]
Hint Unfold lt: bool.
#[ local ] Definition compare (b1 b2 : bool) :=
match b1, b2 with
| false, true => Lt
| true, false => Gt
| _, _ => Eq
end.

Lemma compare_spec : forall b1 b2,
CompareSpec (b1 = b2) (lt b1 b2) (lt b2 b1) (compare b1 b2).