Proposition is_scott_continuous_lub {X Y : hSet} {DX : dcpo_struct X} {DY : dcpo_struct Y} {f : X → Y} (Df : is_scott_continuous DX DY f) {I : UU} {D : I → X} (HD : is_directed DX D) (x : X) (Hx : is_least_upperbound DX D x) : is_least_upperbound DY (λ i, f(D i)) (f x). Proof. exact (pr2 Df I D HD x Hx). 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.