proposition: Lemma monad_to_monoid_laws : monoid_laws M_ENDO monad_to_monoid_data.
proof: Proof. repeat split; apply (nat_trans_eq C); intro c; cbn. - apply Monad_law2. - apply Monad_law1. - rewrite id_left. apply pathsinv0, Monad_law3. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal UniMath.CategoryTheory.Monads.Monads