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(** * Properties mixing [andb] and [orb] *)
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(** Distributivity *)

(* Specifications: *)
Lemma andb_orb_distrib_r :
forall b1 b2 b3:bool, b1 && (b2 || b3) = b1 && b2 || b1 && b3.
Lemma andb_orb_distrib_l :
forall b1 b2 b3:bool, (b1 || b2) && b3 = b1 && b3 || b2 && b3.
Lemma orb_andb_distrib_r :
forall b1 b2 b3:bool, b1 || b2 && b3 = (b1 || b2) && (b1 || b3).
Lemma orb_andb_distrib_l :
forall b1 b2 b3:bool, b1 && b2 || b3 = (b1 || b3) && (b2 || b3).