{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {F : Type u_3} →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : NormedSpace 𝕜 F] →
                FormalMultilinearSeries 𝕜 E F →
                  (k : ℕ) → FormalMultilinearSeries 𝕜 E (ContinuousMultilinearMap 𝕜 (fun i => E) F)