Lemma plusNonnegativeReals_ltcompat : ∏ x y z t : NonnegativeReals, x < y -> z < t -> x + z < y + t. Proof. intros x y z t Hxy Hzt. eapply istrans_ltNonnegativeReals, plusNonnegativeReals_ltcompat_l. - now apply plusNonnegativeReals_ltcompat_r. - exact Hxy. 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.