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] *)

Lemma Zsplit2 n :
{p : Z * Z | let (x1, x2) := p in n = x1 + x2 /\ (x1 = x2 \/ x2 = x1 + 1)}.