Lemma invNonnegativeRationals_ltcompat : ∏ x y : NonnegativeRationals, 0 < x -> x < y -> / y < / x. 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.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.Fields. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim.