Definition least_upper_bound_subtype_is_upper_bound {A : hsubtype P} (x : least_upper_bound_subtype A) {y : P} (A_y : A y) : y ≤ x := least_upper_bound_is_upper_bound x (y,,A_y).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo. Require Import UniMath.OrderTheory.Posets.Subposets.