∀ {P : UpperHalfPlane → Prop} (motive : (∃ z, ∃ (hz : 0 < z.im), P { coe := z, coe_im_pos := hz }) → Prop)
  (x : ∃ z, ∃ (hz : 0 < z.im), P { coe := z, coe_im_pos := hz }),
  (∀ (z : ℂ) (hz : 0 < z.im) (hP : P { coe := z, coe_im_pos := hz }), motive ⋯) → motive x