apply sum_congr rfl
case calc_1
P k : ℕ
x : ℝ
hx : 1 ≤ x
hP : Squarefree P
hx_pos : 0 < x
⊢ (∑ d ∈ P.divisors, if ↑d ≤ x then ↑k ^ ω d / ↑d else 0) =
    ∑ d ∈ P.divisors,
      ∑ a ∈ Fintype.piFinset fun _i => P.divisors,
        if ∏ i : Fin k, a i = d ∧ d ∣ P then if ↑d ≤ x then (↑d)⁻¹ else 0 else 0
case calc_1
P k : ℕ
x : ℝ
hx : 1 ≤ x
hP : Squarefree P
hx_pos : 0 < x
⊢ ∀ x_1 ∈ P.divisors,
    (if ↑x_1 ≤ x then ↑k ^ ω x_1 / ↑x_1 else 0) =
      ∑ a ∈ Fintype.piFinset fun _i => P.divisors,
        if ∏ i : Fin k, a i = x_1 ∧ x_1 ∣ P then if ↑x_1 ≤ x then (↑x_1)⁻¹ else 0 else 0