Lemma actegory_bincoprod_antidistributor_nat_right (v1 v2 : V) (cd : category_binproduct C C) (f : v1 --> v2) : actegory_bincoprod_antidistributor v1 (pr1 cd) (pr2 cd) · f ⊗^{ Act}_{r} bincoproduct_functor BCP cd = #(bincoproduct_functor BCP) (f ⊗^{ actegory_binprod Mon_V Act Act}_{r} cd) · actegory_bincoprod_antidistributor v2 (pr1 cd) (pr2 cd). Proof. apply bincoprod_antidistributor_nat_right. 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.