Lemma NR_to_hr_inside : ∏ x : NonnegativeReals × NonnegativeReals, pr1 (NR_to_hr x) x. Proof. intros x. apply hinhpr ; simpl. exists 0 ; reflexivity. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.NonnegativeRationals.