∀ {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} {A : Type u_4} [inst_5 : NormedRing A] [inst_6 : NormedAlgebra 𝕜 A] [inst_7 : Module A F]
  [inst_8 : IsScalarTower 𝕜 A F] [inst_9 : IsBoundedSMul A F] {i : ℕ} {v : F} {f : E → A},
  ContDiffWithinAt 𝕜 (↑i) f s x →
    UniqueDiffOn 𝕜 s →
      x ∈ s →
        iteratedFDerivWithin 𝕜 i (fun y => f y • v) s x =
          ((ContinuousLinearMap.id 𝕜 A).smulRight v).compContinuousMultilinearMap (iteratedFDerivWithin 𝕜 i f s x)