have l1 : ∀ᶠ n : ℝ in atTop, nnabla (fun n ↦ 1 / d n) n = (d (n + 1) - d n) * (d n)⁻¹ * (d (n + 1))⁻¹ := by
  filter_upwards [l2, l3] with n l2 l3
  rw [nnabla, one_div, one_div, inv_sub_inv l2.ne.symm l3.ne.symm, div_eq_mul_inv, mul_inv, mul_assoc]
n : ℕ
A a b c d✝ u x✝ y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
x : ℝ
hx : 0 < x
d : ℝ → ℝ := fun n => n * ((2 * π) ^ 2 + (n / x).log ^ 2)
l2 : ∀ᶠ (n : ℝ) in atTop, 0 < d n
l3 : ∀ᶠ (n : ℝ) in atTop, 0 < d (n + 1)
⊢ (fun x_1 => nnabla (fun n => 1 / d n) x_1) =O[atTop] fun n => 1 / (n.log ^ 2 * n ^ 2)
n : ℕ
A a b c d✝ u x✝ y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
x : ℝ
hx : 0 < x
d : ℝ → ℝ := fun n => n * ((2 * π) ^ 2 + (n / x).log ^ 2)
l2 : ∀ᶠ (n : ℝ) in atTop, 0 < d n
l3 : ∀ᶠ (n : ℝ) in atTop, 0 < d (n + 1)
l1 : ∀ᶠ (n : ℝ) in atTop, nnabla (fun n => 1 / d n) n = (d (n + 1) - d n) * (d n)⁻¹ * (d (n + 1))⁻¹
⊢ (fun x_1 => nnabla (fun n => 1 / d n) x_1) =O[atTop] fun n => 1 / (n.log ^ 2 * n ^ 2)