Notation Zeven_bool_succ := Z.even_succ (only parsing).
Notation Zeven_bool_pred := Z.even_pred (only parsing).
Notation Zodd_bool_succ := Z.odd_succ (only parsing).
Notation Zodd_bool_pred := Z.odd_pred (only parsing).
(******************************************************************)
(** * Definition of [Z.quot2], [Z.div2] and properties wrt [Zeven] and [Zodd] *)
(** Properties of [Z.div2] *)

(** Properties of [Z.quot2] *)
(** TODO: move to Numbers someday *)
Lemma Zquot2_odd_eqn n : n = 2*(Z.quot2 n) + if Z.odd n then Z.sgn n else 0.