(***************)
(** * Equality *)
(***************)

Definition eqb (b1 b2:bool) : bool :=
  match b1, b2 with
    | true, true => true
    | true, false => false
    | false, true => false
    | false, false => true
  end.

Lemma eqb_true_iff : forall a b:bool, eqb a b = true <-> a = b.