Lemma maxNonnegativeReals_lt : ∏ x y z : NonnegativeReals, x < z -> y < z -> maxNonnegativeReals x y < z. Proof. exact Dcuts_max_lt. Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.