Definition struct_dcpo_laws : hset_struct_laws struct_dcpo_data. Proof. split5. - intro X. apply isaset_dcpo_struct. - intros X Y px py f. apply isaprop_is_scott_continuous. - intros X PX ; cbn in *. apply id_is_scott_continuous. - intros X Y Z PX PY PZ f g Pf Pg. exact (comp_is_scott_continuous Pf Pg). - intros X PX PX' p q ; cbn in *. exact (eq_dcpo_struct _ _ p q). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits.