∀ {𝕜 : Type u_1} [inst : Field 𝕜] {p : 𝕜} {u : AddCircle p}
  (motive : (∃ m < addOrderOf u, m.gcd (addOrderOf u) = 1 ∧ ↑(↑m / ↑(addOrderOf u) * p) = u) → Prop)
  (x : ∃ m < addOrderOf u, m.gcd (addOrderOf u) = 1 ∧ ↑(↑m / ↑(addOrderOf u) * p) = u),
  (∀ (m : ℕ) (hl : m < addOrderOf u) (hg : m.gcd (addOrderOf u) = 1) (he : ↑(↑m / ↑(addOrderOf u) * p) = u), motive ⋯) →
    motive x