proposition: Lemma coprod_antidistributor_nat_right (a1 a2 : A) (cs : power_category I C) (f : A ⟦ a1, a2 ⟧) : bifunctor_coprod_antidistributor a1 cs · f ⊗^{F}_{r} coproduct_functor I CPC cs = #(coproduct_functor I CPD) (fun i => f ⊗^{F}_{r} (cs i)) · bifunctor_coprod_antidistributor a2 cs.
proof: Proof. etrans. { apply postcompWithCoproductArrow. } etrans. 2: { apply pathsinv0, precompWithCoproductArrow. } apply maponpaths; apply funextsec; intro i. etrans. { apply pathsinv0, bifunctor_equalwhiskers. } apply idpath. 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