proposition: 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: Proof. simple refine (_ ,, _). - exact (is_scott_continuous_depfunction_map D fs). - use funextsec. intro. apply strict_scott_continuous_map_on_point. Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.PointedPosets UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous UniMath.OrderTheory.DCPOs.Examples.Propositions UniMath.OrderTheory.DCPOs.Examples.SubDCPO