have {N : ℕ} : (1 : ArithmeticFunction _) N = ∑ d in N.divisors, μ d := by
  rw [← coe_mul_zeta_apply, moebius_mul_coe_zeta]
N : ℕ
hN : 1 ≤ N
⊢ 1 = ↑(∑ m ∈ Icc 1 N, ∑ d ∈ m.divisors, μ d)
N : ℕ
hN : 1 ≤ N
this : ∀ {N : ℕ}, 1 N = ∑ d ∈ N.divisors, μ d
⊢ 1 = ↑(∑ m ∈ Icc 1 N, ∑ d ∈ m.divisors, μ d)