proposition: Lemma Qmult_nonneg_nonpos (x y: Q): 0 <= x -> y <= 0 -> x * y <= 0.
proof: Proof. Proof with auto. unfold Qle. simpl. repeat rewrite Zmult_1_r. intros. rewrite <- (Zmult_0_r (Qnum x)). apply (Zmult_le_compat_l (Qnum y) 0 (Qnum x))... Qed.
imports: Coq.QArith.QArith Coq.ZArith.ZArith Coq.NArith.NArith Coq.QArith.Qpower Coq.QArith.Qround Coq.QArith.Qround Coq.QArith.Qabs CoRN.stdlib_omissions.List