Proposition is_strict_scott_continuous_equalizer_map {W : dcppo} (h : strict_scott_continuous_map W X) (p : (λ w : W, f (h w)) = (λ w : W, g (h w))) : is_strict_scott_continuous W equalizer_dcppo_struct (λ w, h w ,, eqtohomot p w). Proof. simple refine (_ ,, _). - exact (is_scott_continuous_equalizer_map f g h p). - use subtypePath. { intro. apply propproperty. } cbn. apply strict_scott_continuous_map_on_point. 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.