∀ (𝕜 : Type u_5) {ι : Type u_1} (E : ι → Type u_2) (E₁ : ι → Type u_3) (G : Type u_4) [inst : NontriviallyNormedField 𝕜]
  [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)]
  [inst_3 : (i : ι) → SeminormedAddCommGroup (E₁ i)] [inst_4 : (i : ι) → NormedSpace 𝕜 (E₁ i)]
  [inst_5 : SeminormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] [inst_7 : Fintype ι] [inst_8 : DecidableEq ι]
  (f : (i : ι) → E i →L[𝕜] E₁ i) (i : ι) (a : 𝕜) (f₀ : E i →L[𝕜] E₁ i),
  ContinuousMultilinearMap.compContinuousLinearMapL (Function.update f i (a • f₀)) =
    a • ContinuousMultilinearMap.compContinuousLinearMapL (Function.update f i f₀)