Definition Dcuts_plus (X Y : Dcuts) : Dcuts := make_Dcuts (Dcuts_plus_val (pr1 X) (pr1 Y)) (Dcuts_plus_bot (pr1 X) (is_Dcuts_bot X) (pr1 Y) (is_Dcuts_bot Y)) (Dcuts_plus_open (pr1 X) (is_Dcuts_open X) (pr1 Y) (is_Dcuts_open Y)) (Dcuts_plus_corr (pr1 X) (is_Dcuts_bot X) (is_Dcuts_corr X) (pr1 Y) (is_Dcuts_bot Y) (is_Dcuts_corr Y)).
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.