Definition Zdivide_dec:
forall (p q: Z), p > 0 -> { (p|q) } + { ~(p|q) }.
(** Conversion from [Z] to [nat]. *)
Definition nat_of_Z: Z -> nat := Z.to_nat.

Lemma nat_of_Z_max:
forall z, Z.of_nat (nat_of_Z z) = Z.max z 0.