Definition SpecializedGMIt_Thm15 (f : [C, C] ⟦ U Z, U (ptd_from_alg InitAlg) ⟧) : ∃! h : [C, C] ⟦ ℓ (U Z) (pr1 InitAlg), pr1 InitAlg ⟧, # (ℓ (U Z)) (alg_map Id_H InitAlg) · h = pr1 (aux_iso_1 · θ'_Thm15 · aux_iso_2_inv) (pr1 InitAlg) · # (Const_plus_H (U Z)) h · ρ_Thm15 f := (SpecializedGMIt (pr1 InitAlg) (Const_plus_H (U Z)) (ρ_Thm15 f) (aux_iso_1 · θ'_Thm15 · aux_iso_2_inv)).
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Chains.All. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.yoneda. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.PointedFunctorsComposition. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems. Require Import UniMath.SubstitutionSystems.GenMendlerIteration_alt. Require Import UniMath.CategoryTheory.BicatOfCatsElementary. Require Import UniMath.SubstitutionSystems.Notation.