Lemma SumStrength1' : θ_Strength1_int θ. Proof. intro X. apply nat_trans_eq_alt; intro x; simpl. etrans; [apply CoproductOfArrows_comp|]. apply pathsinv0, Coproduct_endo_is_identity; intro i. etrans; [ apply (CoproductOfArrowsIn _ _ (CD (λ i, pr1 (pr1 (H1 i) X) x))) |]. etrans; [| apply id_left]. apply cancel_postcomposition, (nat_trans_eq_pointwise (S11' i X) x). 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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.CategoryTheory.PointedFunctorsComposition. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.SubstitutionSystems.Notation. Require Import UniMath.CategoryTheory.Chains.Chains. Require Import UniMath.CategoryTheory.Chains.OmegaCocontFunctors. Require Import UniMath.CategoryTheory.Limits.Products.