rw [g_0_eq_0, zero_add, sub_zero, dslope_same]
case h.e'_4.h
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 : ‖deriv g 0‖ = 1
h2 : MapsTo g (ball 0 1) (ball (g 0) 1)
h1 : EqOn g (fun z => g 0 + (z - 0) • dslope g 0 0) (ball 0 1)
z : ℂ
⊢ z • deriv g 0 = g 0 + (z - 0) • dslope g 0 0
no goals