proposition: Lemma Qmult_neg_pos (x y : Q) : x < 0 -> 0 < y -> x * y < 0.
proof: Proof. intros H1 H2. apply Qopp_Qlt_0_l. setoid_replace (- (x * y)) with ((- x) * y) by ring. apply Qmult_lt_0_compat; trivial. now apply Qopp_Qlt_0_l. 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