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).

Lemma Zquot2_odd_eqn n : n = 2*(Z.quot2 n) + if Z.odd n then Z.sgn n else 0.