by_cases hl : l ∣ m
l m : ℕ
hm_pos : m > 0
hm : m ∈ {n | Squarefree n}
⊢ (∑ i ∈ m.divisors, μ (m / i) • if l = i then μ l else 0) = if l ∣ m then μ m else 0
case pos
l m : ℕ
hm_pos : m > 0
hm : m ∈ {n | Squarefree n}
hl : l ∣ m
⊢ (∑ i ∈ m.divisors, μ (m / i) • if l = i then μ l else 0) = if l ∣ m then μ m else 0

case neg
l m : ℕ
hm_pos : m > 0
hm : m ∈ {n | Squarefree n}
hl : ¬l ∣ m
⊢ (∑ i ∈ m.divisors, μ (m / i) • if l = i then μ l else 0) = if l ∣ m then μ m else 0