∀ {C D : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] [inst_1 : CategoryTheory.Category.{u_2, u_1} D]
  {F G : CategoryTheory.Functor C D} (e : F ≅ G),
  CategoryTheory.NatTrans.toCatHom₂
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.NatTrans.toCatHom₂ e.hom).toNatTrans
        (CategoryTheory.NatTrans.toCatHom₂ e.inv).toNatTrans) =
    CategoryTheory.NatTrans.toCatHom₂ (CategoryTheory.CategoryStruct.id F.toCatHom.toFunctor)