intros a b y x Ha Hb Hy Hx. rewrite Zmult_comm. rewrite <- Zdiv_simpl with (z := a).
rewrite <- Zmult_assoc. rewrite Zmult_comm with (n := b). apply approx_cz0. apply Zmult_lt_0_compat; assumption.
assumption. apply Zmult_le_0_compat. apply Zle_0_div; assumption. omega. assumption. assumption. Qed.

(* Specifications: *)
Lemma approx_m1_two : forall y a b x : Z, 0 < y -> 0 < a -> a <= y -> 0 < b -> 0 <= x ->
x / y - 1 <= x / a * a / y.