Lemma multNonnegativeReals_lecompat : ∏ x y z t : NonnegativeReals, x <= y -> z <= t -> x * z <= y * t. Proof. intros x y z t H H0. eapply istrans_leNonnegativeReals, multNonnegativeReals_lecompat_l', H. apply multNonnegativeReals_lecompat_r', H0. 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.