proposition: Lemma is_omega_cont_MultiSortedSigToFunctor (sort : UU) (Hsort_set : isaset sort) (C : category) (TC : Terminal C) (IC : Initial C) (BP : BinProducts C) (BC : BinCoproducts C) (PC : forall (I : UU), Products I C) (CC : forall (I : UU), isaset I → Coproducts I C) (M : MultiSortedSig sort) (l : Lims_of_shape conat_graph C) (c : propcoproducts_commute_binproducts C BP (λ p : hProp, CC p (isasetaprop (pr2 p)))) (d : ∏ I : SET, ω_limits_distribute_over_I_coproducts C I l (CC (pr1 I) (pr2 I))) : is_omega_cont (MultiSortedSigToFunctor sort (hlevelntosn 2 _ Hsort_set) C TC BP BC CC M).
proof: Proof. use nat_z_iso_preserve_ωlimits. 3: apply (nat_z_iso_inv (MultiSortedSigToFunctor_test _ _ _ _ _ _ CC _ c)). apply (is_omega_cont_MultiSortedSigToFunctor' sort (hlevelntosn 2 _ Hsort_set) C TC BP BC CC _ d M). Defined.
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 UniMath.SubstitutionSystems.ContinuitySignature.CommutingOfOmegaLimitsAndCoproducts UniMath.SubstitutionSystems.ContinuitySignature.ContinuityOfMultiSortedSigToFunctor UniMath.CategoryTheory.Limits.Preservation