intros c y z Hc Hy Hz. rewrite <- Zdiv_simpl with (z := y). replace (c / y * z * y) with (c / y * y * z).
apply Zle_trans with (c * z / (c * y)). apply Zdiv_le. apply Zmult_lt_0_compat; assumption.
apply Zmult_le_compat_r. rewrite Zmult_comm. apply Z_mult_div_ge. omega. assumption.
do 2 rewrite Zmult_comm with (n := c). rewrite Zdiv_simpl. omega. assumption. assumption. ring.
assumption. assumption. Qed.

Lemma approx_ab_le : forall a b y x : Z, 0 < a -> 0 < b -> 0 < y -> 0 <= x ->
x / a * (a * b / y) / b <= x / a * a / y.