∀ {a : ℕ} (a1 : 1 < a) (motive : ℕ → ℤ√↑(Pell.d✝ a1) → Prop) (x : ℕ) (x_1 : ℤ√↑(Pell.d✝ a1)),
  (∀ (x : ℤ√↑(Pell.d✝ a1)), motive 0 x) → (∀ (n : ℕ) (b : ℤ√↑(Pell.d✝ a1)), motive n.succ b) → motive x x_1