Notation orb_neg_b := orb_negb_r (only parsing).

(* Specifications: *)
Lemma orb_comm : forall b1 b2:bool, b1 || b2 = b2 || b1.
Lemma orb_assoc : forall b1 b2 b3:bool, b1 || (b2 || b3) = b1 || b2 || b3.
Lemma andb_true_iff : forall b1 b2:bool, b1 && b2 = true <-> b1 = true /\ b2 = true.
Lemma andb_false_iff : forall b1 b2:bool, b1 && b2 = false <-> b1 = false \/ b2 = false.
Lemma andb_true_eq : forall a b:bool, true = a && b -> true = a /\ true = b.
Lemma andb_false_intro1 : forall b1 b2:bool, b1 = false -> b1 && b2 = false.
Lemma andb_false_intro2 : forall b1 b2:bool, b2 = false -> b1 && b2 = false.
Lemma andb_false_r : forall b:bool, b && false = false.
Lemma andb_false_l : forall b:bool, false && b = false.