by_cases w_im : w.im = 0
case h.right
w : ℂ
hw : ¬w = 1 ∧ 0 < w.re
⊢ JoinedIn {z | z ≠ 1 ∧ 0 < z.re} 2 w
case pos
w : ℂ
hw : ¬w = 1 ∧ 0 < w.re
w_im : w.im = 0
⊢ JoinedIn {z | z ≠ 1 ∧ 0 < z.re} 2 w

case neg
w : ℂ
hw : ¬w = 1 ∧ 0 < w.re
w_im : ¬w.im = 0
⊢ JoinedIn {z | z ≠ 1 ∧ 0 < z.re} 2 w