(**********************************)
(** * A synonym of [if] on [bool] *)
(**********************************)

Definition ifb (b1 b2 b3:bool) : bool :=
  match b1 with
    | true => b2
    | false => b3
  end.

Lemma negb_andb : forall b1 b2:bool, negb (b1 && b2) = negb b1 || negb b2.