Notation andb_b_false := andb_false_r (only parsing).Notation andb_false_b := andb_false_l (only parsing).

(* Specifications: *)
Lemma andb_diag : forall b, b && b = b.
Lemma andb_true_r : forall b:bool, b && true = b.
Lemma andb_true_l : forall b:bool, true && b = b.