∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : ℕ}
  (f : E →L[𝕜] E →L[𝕜] E [⋀^Fin n]→L[𝕜] F) (v : Fin (n + 2) → E),
  (ContinuousAlternatingMap.alternatizeUncurryFin ((ContinuousAlternatingMap.alternatizeUncurryFinCLM 𝕜 E F).comp f))
      v =
    ∑ i,
      ∑ j ∈ Finset.Ici i,
        (-1) ^ (↑i + ↑j) •
          (((f (v i.castSucc)) (v j.succ)) (j.removeNth (i.castSucc.removeNth v)) -
            ((f (v j.succ)) (v i.castSucc)) (j.removeNth (i.castSucc.removeNth v)))