Proposition eq_dcpo_struct {X : hSet} (DX DX' : dcpo_struct X) (H₁ : is_scott_continuous DX DX' (λ x, x)) (H₂ : is_scott_continuous DX' DX (λ x, x)) : DX = DX'. Proof. use subtypePath. { intro. apply isaprop_directed_complete_poset. } use eq_PartialOrder. - exact (is_scott_continuous_monotone H₁). - exact (is_scott_continuous_monotone H₂). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Core.IntrinsicApartness.