∀ {A : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} A] {B : Type u_6}
  [inst_1 : CategoryTheory.Category.{u_5, u_6} B] {C : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} C]
  (F : CategoryTheory.Functor A B) (G : CategoryTheory.Functor A C) {X Y : A} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (((F.prod' G).comp (CategoryTheory.Prod.snd B C)).map f)
      ((fun x => CategoryTheory.Iso.refl (((F.prod' G).comp (CategoryTheory.Prod.snd B C)).obj x)) Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun x => CategoryTheory.Iso.refl (((F.prod' G).comp (CategoryTheory.Prod.snd B C)).obj x)) X).hom (G.map f)