∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {V W V₁ W₁ : E → E} {s : Set E} {x : E},
  V₁ =ᶠ[nhdsWithin x (insert x s)] V →
    W₁ =ᶠ[nhdsWithin x (insert x s)] W →
      VectorField.lieBracketWithin 𝕜 V₁ W₁ s x = VectorField.lieBracketWithin 𝕜 V W s x