intros y a b x lt_0_y lt_0_a lt_a_y lt_0_b le_0_x lt_x_ab.
apply Zle_trans with (x / a * a / y - 1). cut (x / y - 1 <= x / a * a / y). omega.
apply approx_m1_two with (b := b); assumption. apply approx_m1_one; omega. Qed.

Lemma approx_0_one : forall y a b x : Z, 0 < y -> 0 < a -> 0 < b -> 0 <= x ->
x / a * (a * b / y) / b <= x / a * a / y.