(* Compatibility *)
Notation demorgan1 := andb_orb_distrib_r (only parsing).Notation demorgan2 := andb_orb_distrib_l (only parsing).Notation demorgan3 := orb_andb_distrib_r (only parsing).Notation demorgan4 := orb_andb_distrib_l (only parsing).

(* Specifications: *)
Lemma absorption_andb : forall b1 b2:bool, b1 && (b1 || b2) = b1.
Lemma absorption_orb : forall b1 b2:bool, b1 || b1 && b2 = b1.