Lemma Dcuts_min_bot : Dcuts_def_bot Dcuts_min_val. Proof. intros r Hr q Hqr. split. - apply X_bot with (1 := pr1 Hr), Hqr. - apply Y_bot with (1 := pr2 Hr), Hqr. 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.