intros y a b x lt_0_y lt_0_a lt_0_b le_0_x.
apply Zdiv_le. assumption. rewrite Zmult_comm. apply Z_mult_div_ge. omega. Qed.

Lemma approx_0 : forall y a b x : Z, 0 < y -> 0 < a -> 0 < b -> 0 <= x ->
x / a * (a * b / y) / b <= x / y.