proposition: Lemma Qplus_lt_le_0_compat x y: 0 < x -> 0 <= y -> 0 < x + y.
proof: Proof. Proof with auto. unfold Qlt, Qle. simpl. repeat rewrite Zmult_1_r. intros. apply Z.add_pos_nonneg. apply Zmult_lt_0_compat... reflexivity. apply Zmult_le_0_compat... discriminate. 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