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 Zodd_quot2 n : n >= 0 -> Zodd n -> n = 2 * Z.quot2 n + 1.