simp only [continuousMultilinearCurryFin1_apply, Nat.zero_eq, LinearIsometryEquiv.symm_symm,
  ContinuousLinearMap.coe_comp', ContinuousLinearEquiv.coe_coe, LinearIsometryEquiv.coe_coe,
  Function.comp_apply, ContinuousMultilinearMap.compContinuousLinearMapL_apply,
  continuousMultilinearIsEmptyEquiv_apply,
  ContinuousMultilinearMap.compContinuousLinearMap_apply, Pi.zero_apply, map_zero,
  ContinuousMultilinearMap.curryLeft_apply]
case zero.h
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 m : (i : ι) → M i
⊢ ((continuousMultilinearCurryFin1 𝕜 ((i : ι) → M i) F) (f' x 1)) m =
    (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)))))
      m
case zero.h
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 m : (i : ι) → M i
⊢ (f' x 1) (Fin.snoc 0 m) = (f' x (0 + 1)) (Fin.cons m fun i => 0)