∀ {𝕜 : Type u_3} [inst : NontriviallyNormedField 𝕜] {E : Type u_1} {F : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {p : FormalMultilinearSeries 𝕜 E F} {s : Set E} {x : E}
  (motive : (∃ g, f =ᶠ[nhdsWithin x (insert x s)] g ∧ HasFPowerSeriesAt g p x) → Prop)
  (h : ∃ g, f =ᶠ[nhdsWithin x (insert x s)] g ∧ HasFPowerSeriesAt g p x),
  (∀ (g : E → F) (hfg : f =ᶠ[nhdsWithin x (insert x s)] g) (r : ENNReal) (hg : HasFPowerSeriesOnBall g p x r),
      motive ⋯) →
    motive h