proposition: Lemma bracket_property_parts_identity_nicer_impl2 (h : `T • `T --> `T): bracket_property_parts_identity_nicer h -> bracket_property_parts θ T (identity _) h.
proof: 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.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.Notation