by_cases h_dvd : d ∣ P
s : SelbergSieve
d : ℕ
⊢ ν d * s.selbergWeights d = S⁻¹ * ↑(μ d) * ∑ l ∈ P.divisors, if d ∣ l ∧ ↑l ^ 2 ≤ y then g l else 0
case pos
s : SelbergSieve
d : ℕ
h_dvd : d ∣ P
⊢ ν d * s.selbergWeights d = S⁻¹ * ↑(μ d) * ∑ l ∈ P.divisors, if d ∣ l ∧ ↑l ^ 2 ≤ y then g l else 0

case neg
s : SelbergSieve
d : ℕ
h_dvd : ¬d ∣ P
⊢ ν d * s.selbergWeights d = S⁻¹ * ↑(μ d) * ∑ l ∈ P.divisors, if d ∣ l ∧ ↑l ^ 2 ≤ y then g l else 0