∀ {a : ℕ} (a1 : 1 < a) {x y : ℕ} (motive : (∃ n, { re := ↑x, im := ↑y } = Pell.pellZd a1 n) → Prop)
  (x_1 : ∃ n, { re := ↑x, im := ↑y } = Pell.pellZd a1 n),
  (∀ (m : ℕ) (e : { re := ↑x, im := ↑y } = Pell.pellZd a1 m), motive ⋯) → motive x_1