Lemma plusNonnegativeReals_le_ltcompat : ∏ x y z t : NonnegativeReals, x <= y -> z < t -> x + z < y + t. Proof. intros x y z t Hxy Hzt. eapply istrans_le_lt_ltNonnegativeReals, plusNonnegativeReals_ltcompat_r, Hzt. now apply plusNonnegativeReals_lecompat_l. 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.