proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.CoproductsInActegories UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects