∀ {A : Type u_6} [inst : CategoryTheory.Category.{u_5, u_6} A] {B : Type u_3}
  [inst_1 : CategoryTheory.Category.{u_1, u_3} B] {C : Type u_4} [inst_2 : CategoryTheory.Category.{u_2, u_4} C]
  (F : CategoryTheory.Functor A B) (G : CategoryTheory.Functor A C) (X : A),
  CategoryTheory.Prod.mkHom (F.map (CategoryTheory.CategoryStruct.id X)) (G.map (CategoryTheory.CategoryStruct.id X)) =
    CategoryTheory.CategoryStruct.id (F.obj X, G.obj X)