proposition: 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: 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.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.RealNumbers.Sets UniMath.Algebra.ConstructiveStructures UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.NonnegativeRationals