proposition: Lemma STLC_Functor_Initial : Initial (FunctorAlg STLC_Functor).
proof: Proof. apply SignatureInitialAlgebra. - apply InitialHSET. - apply ColimsHSET_of_shape. - apply is_omega_cocont_MultiSortedSigToSignature. + apply ProductsHSET. + apply Exponentials_functor_HSET. + apply ColimsHSET_of_shape. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.Combinatorics.Lists UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering 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.Monads.Monads UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.Groupoids UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SumOfSignatures UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial_alt UniMath.SubstitutionSystems.SimplifiedHSS.MonadsFromSubstitutionSystems UniMath.SubstitutionSystems.SignatureExamples UniMath.SubstitutionSystems.MultiSorted_alt UniMath.SubstitutionSystems.SimplifiedHSS.MultiSortedMonadConstruction_alt UniMath.SubstitutionSystems.MonadsMultiSorted_alt