#[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_true_iff : forall a b:bool, eqb a b = true <-> a = b.
#[global]
Instance Decidable_eq_bool : forall (x y : bool), Decidable (eq x y) := {
Decidable_spec := eqb_true_iff x y
}.