Lemma le_eqorltNonnegativeRationals : ∏ x y : NonnegativeRationals, x <= y -> (x = y) ⨿ (x < y). Proof. intros x y Hle. generalize (hqlehchoice (pr1 x) (pr1 y) Hle) ; apply sumofmaps ; [intros Hlt | intros Heq]. - right ; exact Hlt. - left. now apply subtypePath_prop, Heq. 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.