proposition: Lemma multNonnegativeRationals_le_lt: ∏ x x' y y' : NonnegativeRationals, 0 < x -> x <= x' -> y < y' -> x * y < x' * y'.
proof: 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.
imports: UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.RealNumbers.Sets UniMath.RealNumbers.Fields UniMath.Algebra.DivisionRig UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim