obtain ⟨r, hf⟩ := hp
case h
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
f : ℂ → E
p : FormalMultilinearSeries ℂ ℂ E
U : Set ℂ
z₀ c : ℂ
n : ℕ
hp : HasFPowerSeriesAt f p z₀
h : p ≠ 0
⊢ ContinuousAt (fun z => (swap dslope z₀)^[FormalMultilinearSeries.order p] f z) z₀
case h.intro
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
f : ℂ → E
p : FormalMultilinearSeries ℂ ℂ E
U : Set ℂ
z₀ c : ℂ
n : ℕ
h : p ≠ 0
r : ENNReal
hf : HasFPowerSeriesOnBall f p z₀ r
⊢ ContinuousAt (fun z => (swap dslope z₀)^[FormalMultilinearSeries.order p] f z) z₀