∀ {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] {V W : E → E}
  {x : E} {f : E → F} {n : WithTop ℕ∞},
  ContDiffAt 𝕜 n f x →
    minSmoothness 𝕜 2 ≤ n →
      DifferentiableAt 𝕜 W x →
        DifferentiableAt 𝕜 V x →
          (fderiv 𝕜 f x) (VectorField.lieBracket 𝕜 V W x) =
            (fderiv 𝕜 (fun x => (fderiv 𝕜 f x) (W x)) x) (V x) - (fderiv 𝕜 (fun x => (fderiv 𝕜 f x) (V x)) x) (W x)