Lemma μ_2_is_Ptd_mor : luinv^{Mon_V}_{I_{Mon_V}} · η ⊗^{Mon_V} η · μ_2 = η. Proof. rewrite assoc'. apply (z_iso_inv_on_right _ _ _ (nat_z_iso_pointwise_z_iso (leftunitor_nat_z_iso Mon_V) I_{ Mon_V})). cbn. rewrite unitors_coincide_on_unit. etrans. 2: { apply pathsinv0, mhss_second_monoidlaw_aux. } rewrite assoc. apply cancel_postcomposition. apply (bifunctor_equalwhiskers Mon_V). 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.