field_simp [two_ne_zero, Real.pi_ne_zero, I_ne_zero]
ι : Type u_1
α : Type u_2
β : Type u_3
U : Set ℂ
c z₀ : ℂ
r : ℝ
f g✝ : ℂ → ℂ
hU : IsOpen U
hcr : closedBall c r ⊆ U
hz₀ : z₀ ∈ ball c r
hf : DifferentiableOn ℂ f U
hfz₀ : f z₀ = 0
hf'z₀ : deriv f z₀ ≠ 0
hfz : ∀ z ∈ closedBall c r, z ≠ z₀ → f z ≠ 0
hr : 0 < r
g : ℂ → ℂ := dslope f z₀
h1 : DifferentiableOn ℂ g U
h2 : ∀ z ∈ closedBall c r, g z ≠ 0
h10 : ∀ z ∈ sphere c r, z - z₀ ≠ 0
this : cindex c r f = ((2 * ↑Real.pi * I)⁻¹ * ∮ (z : ℂ) in C(c, r), (z - z₀)⁻¹) + cindex c r g
⊢ (2 * ↑Real.pi * I)⁻¹ * (2 * ↑Real.pi * I) + 0 = 1
no goals