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

Lemma eqb_false_iff : forall a b:bool, eqb a b = false <-> a <> b.
Definition ifb (b1 b2 b3:bool) : bool :=
match b1 with
| true => b2
| false => b3
end.