Proposition is_strict_scott_continuous_depfunction_map {I : UU} (D : I → dcppo) {W : dcppo} (fs : ∏ (i : I), strict_scott_continuous_map W (D i)) : is_strict_scott_continuous W (depfunction_dcppo D) (λ w i, fs i w). Proof. simple refine (_ ,, _). - exact (is_scott_continuous_depfunction_map D fs). - use funextsec. intro. apply strict_scott_continuous_map_on_point. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous. Require Import UniMath.OrderTheory.DCPOs.Examples.Propositions. Require Import UniMath.OrderTheory.DCPOs.Examples.SubDCPO.