case succ n_ih => exact n_ih ((differentiableOn_dslope (hU.mem_nhds hc)).mpr hf)
E : Type u_1
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
p : FormalMultilinearSeries ℂ ℂ E
U : Set ℂ
z₀ c : ℂ
hU : IsOpen U
hc : c ∈ U
n✝ : ℕ
n_ih : ∀ {f : ℂ → E}, DifferentiableOn ℂ f U → DifferentiableOn ℂ ((swap dslope c)^[n✝] f) U
f : ℂ → E
hf : DifferentiableOn ℂ f U
⊢ DifferentiableOn ℂ ((swap dslope c)^[succ n✝] f) U
no goals