∀ {C D : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Category.{v, u} D]
  (F : CategoryTheory.Functor C D),
  CategoryTheory.NatTrans.toCatHom₂ (CategoryTheory.CategoryStruct.id F) = CategoryTheory.CategoryStruct.id F.toCatHom