case succ k IH =>
  intro n hn hk H
  rcases H.succ_elim (le_trans (by simp) hk) with ⟨n', rfl, H'⟩
  have IH : NuonAux (2 * A + 1) (k + 1) (n' + 1) := IH n' H'.le (le_trans (by simp) hk) H'
  simpa [add_right_comm n' 1] using IH.succ (le_trans hk (by simp [length_two_mul_add_one]))
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚫₀ + 𝛀₁
A k : M
IH : ∀ n ≤ k, k ≤ ‖A‖ → NuonAux A k n → NuonAux (2 * A + 1) (k + 1) (n + 1)
⊢ ∀ n ≤ k + 1, k + 1 ≤ ‖A‖ → NuonAux A (k + 1) n → NuonAux (2 * A + 1) (k + 1 + 1) (n + 1)
no goals