Lemma actegory_bincoprod_antidistributor_commutes_with_associativity_of_coproduct (v : V) (c d e : C) : #(bincoproduct_functor BCP) (catbinprodmor (actegory_bincoprod_antidistributor v c d) (identity (v ⊗_{Act} e))) · actegory_bincoprod_antidistributor v (BCP c d) e · v ⊗^{Act}_{l} bincoprod_associator_data BCP c d e = bincoprod_associator_data BCP (v ⊗_{Act} c) (v ⊗_{Act} d) (v ⊗_{Act} e) · #(bincoproduct_functor BCP) (catbinprodmor (identity (v ⊗_{Act} c)) (actegory_bincoprod_antidistributor v d e)) · actegory_bincoprod_antidistributor v c (BCP d e). Proof. apply bincoprod_antidistributor_commutes_with_associativity_of_coproduct. 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.