Lemma nat_to_hr_O : nat_to_hr O = 0%ring. Proof. unfold nat_to_hr. rewrite nat_to_NonnegativeReals_O. 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.