case inl => assumption
ι : Type u_1
F : ι → ℂ → ℂ
f : ℂ → ℂ
z₀ : ℂ
p : Filter ι
r : ℝ
U : Set ℂ
inst✝ : NeBot p
hU : IsOpen U
F_holo : ∀ᶠ (n : ι) in p, DifferentiableOn ℂ (F n) U
F_noz : ∀ (n : ι), ∀ z ∈ U, F n z ≠ 0
F_conv : TendstoLocallyUniformlyOn F f p U
hz₀ : z₀ ∈ U
hfz₀ : f z₀ = 0
H1 : AnalyticAt ℂ f z₀
h✝ : ∀ᶠ (z : ℂ) in 𝓝 z₀, f z = 0
⊢ ∀ᶠ (z : ℂ) in 𝓝 z₀, f z = 0
no goals