Lemma islbub_Dcuts_of_Dcuts (E : hsubtype Dcuts) E_bot E_corr : isSmallerThanUpperBounds (X := PreorderedSetEffectiveOrder eo_Dcuts) E (Dcuts_of_Dcuts E E_bot E_corr). Proof. intros. intros x Hx ; simpl. intros r ; apply hinhuniv ; intros y. generalize (Hx _ (pr1 (pr2 y))). intros H ; simple refine (H _ _). exact (pr2 (pr2 y)). 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.