proposition: 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: Proof. apply bincoprod_antidistributor_nat. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.ProductCategory