proposition: Proposition cartesian_closed_struct_dcppo_laws : closed_under_fun_laws cartesian_closed_struct_dcppo_data.
proof: Proof. split. - intros X Y DX DY ; cbn in *. exact (is_scott_continuous_eval (X ,, pr1 DX) (Y ,, pr1 DY)). - intros X Y Z DX DY DZ f Df ; cbn in *. apply (@is_scott_continuous_lam (X ,, pr1 DX) (Y ,, pr1 DY) (Z ,, pr1 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.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits