Lemma multNonnegativeRationals_le_lt: ∏ x x' y y' : NonnegativeRationals, 0 < x -> x <= x' -> y < y' -> x * y < x' * y'. Proof. intros x x' y y' Hx0 Hx Hy. apply istrans_lt_le_ltNonnegativeRationals with (x* y'). - apply multNonnegativeRationals_ltcompat_l. + exact Hx0. + exact Hy. - now apply multNonnegativeRationals_lecompat_r, Hx. 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.