fact: Definition coproduct_of_functors_omega_cont (C : category) (F : (pr1 I) → C ⟶ D) (ω_distr : ω_limits_distribute_over_I_coproducts D I ω_lim CP) : (∏ i : pr1 I, is_omega_cont (F i)) -> is_omega_cont (coproduct_of_functors _ _ _ CP F).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.Lists UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.Groupoids UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SumOfSignatures UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.MultiSorted_alt UniMath.CategoryTheory.Chains.OmegaContFunctors UniMath.SubstitutionSystems.ContinuitySignature.GeneralLemmas