proposition: Lemma multNonnegativeRationals_ltcompat_l : ∏ k x y : NonnegativeRationals, 0 < k -> (x < y) <-> (k * x < k * y).
proof: Proof. intros k x y Hk. split ; intro H. - apply (hqlthandmultl (pr1 x) (pr1 y) (pr1 k)). + exact Hk. + exact H. - apply (hqlthandmultlinv (pr1 x) (pr1 y) (pr1 k)). + exact Hk. + exact H. Qed.
imports: UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.RealNumbers.Sets UniMath.RealNumbers.Fields UniMath.Algebra.DivisionRig UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim