Lemma bincoprod_antidistributor_nat_left (a : A) (cc'1 cc'2 : category_binproduct C C) (g : category_binproduct C C ⟦ cc'1, cc'2 ⟧) : bifunctor_bincoprod_antidistributor a (pr1 cc'1) (pr2 cc'1) · a ⊗^{F}_{l} #(bincoproduct_functor BCPC) g = #(bincoproduct_functor BCPD) (#(pair_functor (leftwhiskering_functor F a) (leftwhiskering_functor F a)) g) · bifunctor_bincoprod_antidistributor a (pr1 cc'2) (pr2 cc'2). Proof. apply bincoprod_antidistributor_nat. 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.Isos. Require Import  UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.ProductCategory. Import BifunctorNotations. Import BifunctorNotations. Section FunctorsFromProductCategory. Import BifunctorNotations. End FunctorsFromProductCategory. Import BifunctorNotations. Import BifunctorNotations. Import BifunctorNotations.