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_plus:
forall p q,
p >= 0 -> q >= 0 ->
nat_of_Z (p + q) = (nat_of_Z p + nat_of_Z q)%nat.