#[global]
Hint Resolve andb_prop_elim: bool.
Notation andb_prop2 := andb_prop_elim (only parsing).

(** Rewrite rules about andb, orb and if (used in romega) *)
Lemma andb_if : forall (A:Type)(a a':A)(b b' : bool),
(if b && b' then a else a') =
(if b then if b' then a else a' else a').