proposition: Proposition is_scott_continuous_depfunction_pr (i : I) : is_scott_continuous depfunction_dcpo (D i) (λ f, f i).
proof: Proof. use make_is_scott_continuous. - exact (is_monotone_depfunction_poset_pr (λ i, D i) (λ i, D i) i). - intros E. cbn ; unfold type_prod_pointwise_lub. use antisymm_dcpo. + use dcpo_lub_is_least ; cbn. intro e. use less_than_dcpo_lub ; [ exact e | ] ; cbn. apply refl_dcpo. + use dcpo_lub_is_least ; cbn. intro e. use less_than_dcpo_lub ; [ exact e | ] ; cbn. apply refl_dcpo. 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