proposition: Lemma Dcuts_mult_lecompat_l : ∏ x y z: Dcuts, (0 < x) -> (Dcuts_mult y x <= Dcuts_mult z x) -> (y <= z).
proof: Proof. intros x y z Hx0. intros H ; apply Dcuts_nlt_ge ; intro H0 ; apply (pr2 (Dcuts_nlt_ge _ _) H). now apply Dcuts_mult_ltcompat_l. Qed.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.RealNumbers.Sets UniMath.Algebra.ConstructiveStructures UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.NonnegativeRationals