by_cases hx : x = 0
x : ℤ
⊢ UniqueFactorizationMonoid.normalizedFactors x =
    Multiset.filter (Eq 2) (UniqueFactorizationMonoid.normalizedFactors x) + oddFactors x
case pos
x : ℤ
hx : x = 0
⊢ UniqueFactorizationMonoid.normalizedFactors x =
    Multiset.filter (Eq 2) (UniqueFactorizationMonoid.normalizedFactors x) + oddFactors x

case neg
x : ℤ
hx : ¬x = 0
⊢ UniqueFactorizationMonoid.normalizedFactors x =
    Multiset.filter (Eq 2) (UniqueFactorizationMonoid.normalizedFactors x) + oddFactors x