(** * Division on Z. *)
Definition ZDivides (x y : Z) : Prop := exists q : Z, y = (x * q)%Z.

Theorem zdiv_rem :
forall d n : Z,
(d > 0)%Z ->
exists q : Z, (exists r : Z, (0 <= r < d)%Z /\ n = (q * d + r)%Z).