Lemma islub_Dcuts_of_Dcuts (E : hsubtype eo_Dcuts) E_bot E_corr : isLeastUpperBound (X := PreorderedSetEffectiveOrder eo_Dcuts) E (Dcuts_of_Dcuts E E_bot E_corr). Proof. split. - exact (isub_Dcuts_of_Dcuts E E_bot E_corr). - exact (islbub_Dcuts_of_Dcuts E E_bot E_corr). 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.