Lemma invNonnegativeRationals_ltcompat' : ∏ x y : NonnegativeRationals, 0 < y -> / y < / x -> x < y. Proof. intros x y Hy0 Hxy. rewrite <- (isinvolutive_invNonnegativeRationals x), <- (isinvolutive_invNonnegativeRationals y). apply invNonnegativeRationals_ltcompat. - apply ispositive_invNonnegativeRationals. exact Hy0. - exact Hxy. 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.