∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E}
  {x : E} {i : ℕ} {f g : E → F},
  ContDiffWithinAt 𝕜 (↑i) f s x →
    ContDiffWithinAt 𝕜 (↑i) g s x →
      UniqueDiffOn 𝕜 s →
        x ∈ s →
          iteratedFDerivWithin 𝕜 i (fun i => f i + g i) s x =
            iteratedFDerivWithin 𝕜 i f s x + iteratedFDerivWithin 𝕜 i g s x