rewrite Z_div_mult. trivial. omega. assumption. assumption. Qed.

(* Specifications: *)
Lemma Zdiv_den_le : forall x y z : Z, 0 <= x -> 0 < z -> z <= y -> x / y <= x / z.
intros x y z H H0 H1. rewrite <- Zdiv_simpl with (y := y) (z := z).