Lemma plusNonnegativeReals_lecompat : ∏ x y x' y' : NonnegativeReals, x <= y -> x' <= y' -> x + x' <= y + y'. Proof. intros x y x' y' H H'. refine (istrans_leNonnegativeReals _ _ _ _ _). - apply plusNonnegativeReals_lecompat_l. apply H. - apply plusNonnegativeReals_lecompat_r. exact H'. 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.