proposition: Lemma Dcuts_max_min : ∏ x y : Dcuts, Dcuts_max x (Dcuts_min x y) = x.
proof: Proof. intros x y. apply Dcuts_eq_is_eq ; intros r. split. - apply hinhuniv ; apply sumofmaps ; [intros Xr | intros Hr]. + exact Xr. + exact (pr1 Hr). - intros Xr. apply hinhpr. now 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