(** Boolean tests of parity (now in BinInt.Z) *)
Notation Zeven_bool := Z.even (only parsing).
Notation Zodd_bool := Z.odd (only parsing).

Lemma Zodd_bool_iff n : Z.odd n = true <-> Zodd n.
Ltac boolify_even_odd := rewrite <- ?Zeven_bool_iff, <- ?Zodd_bool_iff.