Lemma Dcuts_le_ge_eq : ∏ x y : Dcuts, x <= y -> x >= y -> x = y. Proof. intros x y le_xy ge_xy. apply Dcuts_eq_is_eq. split. - now refine (le_xy _). - now refine (ge_xy _). Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.