Definition equalizer_dcpo_struct : dcpo_struct (∑ (x : X), hProp_to_hSet (f x = g x)%logic)%set. Proof. simple refine (_ ,, _). - exact (Equalizer_order X _ f g). - exact directed_complete_equalizer. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous.