Definition equalizer_lub (D : directed_set (Equalizer_order X Y f g)) : lub (Equalizer_order X Y f g) D. Proof. use make_lub. - exact (⨆ Equalizer_directed_set D ,, equalizer_lub_path D). - exact (is_lub_equalizer_lub D). 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.