rewrite <- Zdiv_simpl with (y := z) (z := y). rewrite Zmult_comm with (n := y).
apply Zdiv_le. apply Zmult_lt_0_compat; omega. apply Zmult_le_compat_l; omega. assumption. omega. omega.
assumption. Qed.

Lemma approx_cz : forall c y z : Z, 0 < c -> 0 < y -> 0 <= z -> z <= c ->
z / y - c / y * z / c <= 1.