proposition: 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: 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.
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