Definition Dcuts_plus_val : hsubtype NonnegativeRationals := λ r : NonnegativeRationals, ((X r) ⨿ (Y r)) ∨ (∑ xy : NonnegativeRationals × NonnegativeRationals, (r = (pr1 xy + pr2 xy)%NRat) × ((X (pr1 xy)) × (Y (pr2 xy)))).
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.