Notation andb_b_true := andb_true_r (only parsing).Notation andb_true_b := andb_true_l (only parsing).

(* Specifications: *)
Lemma andb_false_elim : forall b1 b2:bool, b1 && b2 = false -> {b1 = false} + {b2 = false}.
Lemma andb_negb_r : forall b:bool, b && negb b = false.
Lemma andb_negb_l : forall b:bool, negb b && b = false.