Lemma actegory_coprod_antidistributor_nat_left (v : V) (cs1 cs2 : power_category I C) (g : cs1 --> cs2) : actegory_coprod_antidistributor v cs1 · v ⊗^{Act}_{l} #(coproduct_functor I CP) g = #(coproduct_functor I CP) (v ⊗^{actegory_power Mon_V I Act}_{l} g) · actegory_coprod_antidistributor v cs2. Proof. apply coprod_antidistributor_nat_left. 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.