Definition equalizer_dcppo_struct : dcppo_struct (∑ (x : X), hProp_to_hSet (f x = g x)%logic)%set. Proof. simple refine (equalizer_dcpo_struct f g ,, (⊥_{X} ,, _) ,, _). - abstract (cbn ; refine (strict_scott_continuous_map_on_point f @ !_) ; apply (strict_scott_continuous_map_on_point g)). - abstract (cbn ; intros xp ; apply is_min_bottom_dcppo). 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.