Lemma θ_Strength1_int_nicer_implies_θ_Strength1_int : θ_Strength1_int_nicer → θ_Strength1_int. Proof. intros T X. rewrite T. etrans. { apply maponpaths. apply (functor_id H X). } apply id_right. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.BicatOfCatsElementary. Require Import UniMath.SubstitutionSystems.Notation.