proposition: Proposition cartesian_closed_struct_dcpo_laws : closed_under_fun_laws cartesian_closed_struct_dcpo_data.
proof: Proof. split. - intros X Y DX DY ; cbn in *. exact (is_scott_continuous_eval (X ,, DX) (Y ,, DY)). - intros X Y Z DX DY DZ f Df ; cbn in *. apply (@is_scott_continuous_lam (X ,, DX) (Y ,, DY) (Z ,, DZ) (f ,, Df)). Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.DCPOs UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits