proposition: Lemma bincoprod_antidistributor_nat_right (a1 a2 : A) (cc' : category_binproduct C C) (f : A ⟦ a1, a2 ⟧) : bifunctor_bincoprod_antidistributor a1 (pr1 cc') (pr2 cc') · f ⊗^{F}_{r} bincoproduct_functor BCPC cc' = #(bincoproduct_functor BCPD) (catbinprodmor (f ⊗^{F}_{r} (pr1 cc')) (f ⊗^{F}_{r} (pr2 cc'))) · bifunctor_bincoprod_antidistributor a2 (pr1 cc') (pr2 cc').
proof: Proof. etrans. { apply postcompWithBinCoproductArrow. } etrans. 2: { apply pathsinv0, precompWithBinCoproductArrow. } apply maponpaths_12. - etrans. { apply pathsinv0, bifunctor_equalwhiskers. } apply idpath. - 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