intro g
f g : ℂ → ℂ
p : FormalMultilinearSeries ℂ ℂ ℂ
z z₀ c : ℂ
n : ℕ
U : Set ℂ
r : ℝ
hp : HasFPowerSeriesAt f p z₀
h : p ≠ 0
⊢ let g := (swap dslope z₀)^[FormalMultilinearSeries.order p] f;
  ∀ᶠ (z : ℂ) in 𝓝 z₀, z ≠ z₀ → deriv f z / f z = ↑(FormalMultilinearSeries.order p) / (z - z₀) + deriv g z / g z
f g✝ : ℂ → ℂ
p : FormalMultilinearSeries ℂ ℂ ℂ
z z₀ c : ℂ
n : ℕ
U : Set ℂ
r : ℝ
hp : HasFPowerSeriesAt f p z₀
h : p ≠ 0
g : ℂ → ℂ := (swap dslope z₀)^[FormalMultilinearSeries.order p] f
⊢ ∀ᶠ (z : ℂ) in 𝓝 z₀, z ≠ z₀ → deriv f z / f z = ↑(FormalMultilinearSeries.order p) / (z - z₀) + deriv g z / g z