proposition: Lemma coprod_antidistributor_triangle_identity (cs : power_category I C) : #(coproduct_functor I CP) au^{actegory_power Mon_V I Act}_{cs} = actegory_coprod_antidistributor I_{Mon_V} cs · au^{Act}_{coproduct_functor I CP cs}.
proof: Proof. etrans. 2: { apply pathsinv0, postcompWithCoproductArrow. } cbn. unfold CoproductOfArrows. apply maponpaths, funextsec; intro i; apply pathsinv0, actegory_unitornat. 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.Functors UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.ProductActegory UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts