Proposition is_strict_scott_continuous_equalizer_pr1 : is_strict_scott_continuous equalizer_dcppo_struct X pr1. Proof. simple refine (_ ,, _). - exact (is_scott_continuous_equalizer_pr1 f g). - apply idpath. Qed.
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.