proposition: Lemma Dcuts_max_carac_l : ∏ x y : Dcuts, y <= x -> Dcuts_max x y = x.
proof: Proof. intros x y Hxy. apply Dcuts_eq_is_eq ; intros r ; split. - apply hinhuniv ; apply sumofmaps ; [ intros Xr | intros Yr ]. + exact Xr. + now refine (Hxy _ _). - intros Xr. now apply hinhpr ; left. 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