proposition: Lemma STLC_Functor_Initial : Initial (FunctorAlg STLC_Functor).
proof: Proof. apply SignatureInitialAlgebraSetSort. apply is_omega_cocont_MultiSortedSigToSignature. apply slice_precat_colims_of_shape, ColimsHSET_of_shape. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.Combinatorics.Lists UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Slice UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.slicecat UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.LiftingInitial_alt UniMath.SubstitutionSystems.Notation UniMath.SubstitutionSystems.MonadsMultiSorted UniMath.SubstitutionSystems.MultiSorted UniMath.SubstitutionSystems.MultiSortedMonadConstruction