rw [LinearIsometryEquiv.comp_hasFDerivAt_iff']
case zero
ι : Type u_1
𝕜 : Type u_2
inst✝⁸ : Fintype ι
inst✝⁷ : DecidableEq ι
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_3
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
M : ι → Type u_4
inst✝³ : (i : ι) → NormedAddCommGroup (M i)
inst✝² : (i : ι) → NormedSpace 𝕜 (M i)
F : Type u_5
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
f : ((i : ι) → M i) → F
f' : ((i : ι) → M i) → FormalMultilinearSeries 𝕜 ((i : ι) → M i) F
hf : HasFTaylorSeriesUpTo (↑Nat.zero + 1) f f'
js : Fin Nat.zero → ι
x : (i : ι) → M i
⊢ HasFDerivAt (⇑(LinearIsometryEquiv.symm (continuousMultilinearIsEmptyEquiv 𝕜 (fun i => M (js i)) F)) ∘ f)
    (ContinuousLinearMap.comp
      (ContinuousMultilinearMap.compContinuousLinearMapL fun i => ContinuousLinearMap.single (js i))
      (ContinuousMultilinearMap.curryLeft (f' x (Nat.zero + 1))))
    x
case zero
ι : Type u_1
𝕜 : Type u_2
inst✝⁸ : Fintype ι
inst✝⁷ : DecidableEq ι
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_3
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
M : ι → Type u_4
inst✝³ : (i : ι) → NormedAddCommGroup (M i)
inst✝² : (i : ι) → NormedSpace 𝕜 (M i)
F : Type u_5
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace 𝕜 F
f : ((i : ι) → M i) → F
f' : ((i : ι) → M i) → FormalMultilinearSeries 𝕜 ((i : ι) → M i) F
hf : HasFTaylorSeriesUpTo (↑Nat.zero + 1) f f'
js : Fin Nat.zero → ι
x : (i : ι) → M i
⊢ HasFDerivAt f
    (ContinuousLinearMap.comp
      (↑(ContinuousLinearEquiv.mk
          (LinearIsometryEquiv.symm
              (LinearIsometryEquiv.symm (continuousMultilinearIsEmptyEquiv 𝕜 (fun i => M (js i)) F))).toLinearEquiv))
      (ContinuousLinearMap.comp
        (ContinuousMultilinearMap.compContinuousLinearMapL fun i => ContinuousLinearMap.single (js i))
        (ContinuousMultilinearMap.curryLeft (f' x (Nat.zero + 1)))))
    x