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. etrans. 2: { apply pathsinv0, postcompWithBinCoproductArrow. } cbn. unfold BinCoproductOfArrows. apply maponpaths_12; apply pathsinv0, actegory_unitornat. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Actegories.ProductActegory. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.