Proposition is_scott_continuous_constant {X Y : hSet} (DX : dcpo_struct X) (DY : dcpo_struct Y) (y : Y) : is_scott_continuous DX DY (λ _, y). Proof. split. - intros x₁ x₂ p. apply refl_PartialOrder. - intros I D HD x HX. split. + intro i. apply refl_PartialOrder. + intros z Hz. cbn in *. induction HD as [ i HD ]. revert i. use factor_through_squash. { apply propproperty. } exact Hz. 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.