Lemma bracket_property_parts_identity_nicer_impl1 (h : `T • `T --> `T): bracket_property_parts θ T (identity _) h -> bracket_property_parts_identity_nicer h. Proof. intro Hyp. induction Hyp as [Hyp1 Hyp2]. split. - etrans. 2: { exact Hyp1. } apply nat_trans_eq_alt. intro c. apply idpath. - etrans. { exact Hyp2. } apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. 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.Notation.