Lemma mhss_third_monoidlaw_aux : θ (pr1 mh_squared,, pr2 mh_squared) gh · # H (μ ⊗^{Mon_V}_{r} gh) = μ_2 ⊗^{Mon_V}_{r} H gh · θ Ptd_from_mhss gh. Proof. apply pathsinv0. assert (aux := lineator_linnatright Mon_PtdV (actegory_with_canonical_pointed_action Mon_V) (actegory_with_canonical_pointed_action Mon_V) H θ mh_squared Ptd_from_mhss gh μ_2_Ptd). simpl in aux. etrans. { exact aux. } apply idpath. 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.