Lemma minusNonnegativeRationals_eq_zero: ∏ x y : NonnegativeRationals, x <= y -> x - y = 0. Proof. intros x y Hle. unfold minusNonnegativeRationals, hnnq_minus. generalize (hqgthorleh (pr1 x) (pr1 y)). apply coprod_rect ; intros H. - apply fromempty. exact (Hle H). - reflexivity. 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.