rw [normSq_eq_abs]
z u✝ z₀ : ℂ
U : Set ℂ
inst✝ : good_domain U
f : ℂ → ℂ
f_diff : DifferentiableOn ℂ f 𝔻
f_img : MapsTo f 𝔻 𝔻
f_noninj : ¬InjOn f 𝔻
u : ℂ := f 0
u_in_𝔻 : u ∈ 𝔻
g : ℂ → ℂ := (φ u_in_𝔻).to_fun ∘ f
g_diff : DifferentiableOn ℂ g 𝔻
g_maps : MapsTo g 𝔻 𝔻
g_0_eq_0 : g 0 = 0
h : ¬Complex.abs (deriv g 0) = 1
g'0_le_1 : Complex.abs (deriv g 0) ≤ 1
g'0_lt_1 : Complex.abs (deriv g 0) < 1
g'0_eq_mul : deriv g 0 = deriv (φ u_in_𝔻).to_fun u * deriv f 0
e1 : 1 - ↑(normSq u) ≠ 0
φ'u_u : deriv (φ u_in_𝔻).to_fun u = 1 / (1 - ↑(normSq u))
e2 : 0 ≤ normSq u
⊢ normSq u < 1
z u✝ z₀ : ℂ
U : Set ℂ
inst✝ : good_domain U
f : ℂ → ℂ
f_diff : DifferentiableOn ℂ f 𝔻
f_img : MapsTo f 𝔻 𝔻
f_noninj : ¬InjOn f 𝔻
u : ℂ := f 0
u_in_𝔻 : u ∈ 𝔻
g : ℂ → ℂ := (φ u_in_𝔻).to_fun ∘ f
g_diff : DifferentiableOn ℂ g 𝔻
g_maps : MapsTo g 𝔻 𝔻
g_0_eq_0 : g 0 = 0
h : ¬Complex.abs (deriv g 0) = 1
g'0_le_1 : Complex.abs (deriv g 0) ≤ 1
g'0_lt_1 : Complex.abs (deriv g 0) < 1
g'0_eq_mul : deriv g 0 = deriv (φ u_in_𝔻).to_fun u * deriv f 0
e1 : 1 - ↑(normSq u) ≠ 0
φ'u_u : deriv (φ u_in_𝔻).to_fun u = 1 / (1 - ↑(normSq u))
e2 : 0 ≤ normSq u
⊢ Complex.abs u ^ 2 < 1