proposition: Lemma multNonnegativeRationals_lecompat_l : ∏ k x y : NonnegativeRationals, x <= y -> k * x <= k * y.
proof: Proof. intros k x y Hle. generalize (eq0orgt0NonnegativeRationals k) ; apply sumofmaps ; intros Hk0. - rewrite Hk0. rewrite !islabsorb_zero_multNonnegativeRationals. now apply isrefl_leNonnegativeRationals. - apply hqlehandmultl, Hle. exact Hk0. 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