proposition: Lemma bincoprod_antidistributor_triangle_identity (cd : category_binproduct C C) : #(bincoproduct_functor BCP) au^{actegory_binprod Mon_V Act Act}_{cd} = actegory_bincoprod_antidistributor I_{Mon_V} (pr1 cd) (pr2 cd) · au^{Act}_{bincoproduct_functor BCP cd}.
proof: Proof. etrans. 2: { apply pathsinv0, postcompWithBinCoproductArrow. } cbn. unfold BinCoproductOfArrows. apply maponpaths_12; 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