∀ {𝕜 : Type u_5} {E : Type u_2} {F : Type u_3} (G : Type u_4) {ι : Type u_1} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : SeminormedAddCommGroup F]
  [inst_4 : NormedSpace 𝕜 F] [inst_5 : SeminormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] [inst_7 : Fintype ι]
  [inst_8 : DecidableEq ι] (g : E →L[𝕜] F) (f₁ f₂ : F [⋀^ι]→L[𝕜] G),
  (f₁ + f₂).fderivCompContinuousLinearMap g = f₁.fderivCompContinuousLinearMap g + f₂.fderivCompContinuousLinearMap g