proposition: Lemma is_omega_cocont_Lam (hE : ∏ x, is_omega_cocont (constprod_functor1 (BinProducts_functor_precat C C CP) x)) (LC : Colims_of_shape nat_graph C) : is_omega_cocont (Signature_Functor Lam_Sig).
proof: Proof. apply is_omega_cocont_BinCoproduct_of_functors. - apply (is_omega_cocont_App_H hE). - apply (is_omega_cocont_Abs_H LC). 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