∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {x : M} {V W : (x : M) → TangentSpace I x} {c : 𝕜}
  [inst_6 : IsManifold I 2 M] [CompleteSpace E],
  MDifferentiableAt I I.tangent (fun x => { proj := x, snd := V x }) x →
    VectorField.mlieBracket I (c • V) W x = c • VectorField.mlieBracket I V W x