Definition SpecializedGMIt_Thm15 (Z: Ptd)(f : [C, C] ⟦ U Z, U (ptd_from_alg InitAlg) ⟧) : ∃! h : [C, C] ⟦ ℓ (U Z) (` (InitialObject IA)), pr1 InitAlg ⟧, # (ℓ (U Z)) (alg_map Id_H (InitialObject IA)) · h = pr1 ((aux_iso_1 Z · θ'_Thm15 Z · aux_iso_2_inv Z)) (` (InitialObject IA)) · # (Const_plus_H (U Z)) h · ρ_Thm15 Z f := SpecializedGMIt Z (pr1 InitAlg) (Const_plus_H (U Z)) (ρ_Thm15 Z f) (aux_iso_1 Z · θ'_Thm15 Z · aux_iso_2_inv Z).
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.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. Require Import UniMath.CategoryTheory.RightKanExtension. Require Import UniMath.SubstitutionSystems.GenMendlerIteration. Require Import UniMath.CategoryTheory.BicatOfCatsElementary. Require Import UniMath.SubstitutionSystems.Notation.