∀ {𝕜 : Type u_1} {ι : Type u_2} {E : Type u_3} {G : Type u_5} {H : Type u_6} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G]
  [inst_5 : NormedAddCommGroup H] [inst_6 : NormedSpace 𝕜 H] {f : E → G [⋀^ι]→L[𝕜] H} {f' : E →L[𝕜] G [⋀^ι]→L[𝕜] H}
  {x : E} [Finite ι],
  HasStrictFDerivAt (ContinuousAlternatingMap.toContinuousMultilinearMap ∘ f)
      ((ContinuousAlternatingMap.toContinuousMultilinearMapCLM 𝕜).comp f') x ↔
    HasStrictFDerivAt f f' x