proposition: Lemma invNonnegativeRationals_ltcompat : ∏ x y : NonnegativeRationals, 0 < x -> x < y -> / y < / x.
proof: Proof. intros x y Hx0 Hxy. apply notge_ltNonnegativeRationals. intros H ; revert Hxy. change (neg (x < y)). apply notlt_geNonnegativeRationals. apply invNonnegativeRationals_lecompat'. - exact Hx0. - 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