Lemma θ_Strength2_int_from_δ : θ_Strength2_int θ_from_δ. Proof. intros F Ze Ze'; simpl. set (Z := pr1 Ze); set (Z' := pr1 Ze'). apply nat_trans_eq; [apply homset_property |] ; intro c; simpl. generalize (nat_trans_eq_pointwise (distributive_law2 G DL Ze Ze') c); simpl. rewrite !id_left, !id_right; intro H. etrans; [apply maponpaths, H|]. apply functor_comp. Qed.
Require Import UniMath.Foundations.PartD. 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.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.CategoryTheory.BicatOfCatsElementary. Require Import UniMath.SubstitutionSystems.Notation. Require Import UniMath.CategoryTheory.PointedFunctorsComposition.