Lemma multNonnegativeRationals_lt_le: ∏ x x' y y' : NonnegativeRationals, 0 < y -> x < x' -> y <= y' -> x * y < x' * y'. Proof. intros x x' y y' Hy0 Hx Hy. apply istrans_lt_le_ltNonnegativeRationals with (x' * y). - apply multNonnegativeRationals_ltcompat_r. + exact Hy0. + exact Hx. - now apply multNonnegativeRationals_lecompat_l, Hy. Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.Fields. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim.