proposition: 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: Proof. apply bincoprod_antidistributor_commutes_with_associativity_of_coproduct. 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