proposition: Lemma is_omega_cocont_App_H (hE : ∏ x, is_omega_cocont (constprod_functor1 (BinProducts_functor_precat C C CP) x)) : is_omega_cocont App_H.
proof: Proof. unfold App_H, square_functor. apply is_omega_cocont_BinProduct_of_functors; try assumption. - apply (BinProducts_functor_precat _ _ CP). - apply is_omega_cocont_functor_identity. - apply is_omega_cocont_functor_identity. Defined.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.CategoryTheory.PrecategoryBinProduct UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.BinSumOfSignatures UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.OmegaCocontFunctors UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Colimits