Qed.

(* Specifications: *)
Lemma Zlt_mult_l :
forall p q r : Z, (0 < r)%Z -> (p < q)%Z -> (r * p < r * q)%Z.
Lemma Zle_mult_l :
forall p q r : Z, (0 < r)%Z -> (p <= q)%Z -> (r * p <= r * q)%Z.