Lemma mhss_second_monoidlaw_aux : ru^{Mon_V}_{I_{Mon_V}} · η = I_{Mon_V} ⊗^{Mon_V}_{l} η · (η ⊗^{Mon_V}_{r} gh · μ). Proof. rewrite assoc. etrans. 2: { apply cancel_postcomposition. apply (bifunctor_equalwhiskers Mon_V). } unfold functoronmorphisms1. rewrite assoc'. etrans. 2: { apply maponpaths. apply pathsinv0, mhss_first_monoidlaw. } apply pathsinv0, monoidal_rightunitornat. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Actegories.CoproductsInActegories. Require Import UniMath.CategoryTheory.coslicecat. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Import BifunctorNotations. Import MonoidalNotations.