proposition: Lemma Qlt_reg_mult_pos_l: forall x y z : Q, Zero < x -> y < z -> x * y < x * z.
proof: Proof. intros x y z Hx Hyz; apply Qlt_Zero_Qminus; stepr (x*(z-y)); try ring; apply Qlt_mult_pos_pos; trivial; apply Qlt_Qminus_Zero; assumption. Qed.