apply Multiset.eq_zero_of_forall_not_mem
case h₁
g : Multiset ℤ
hg : ∀ (x : ℤ), x ∈ g → OddPrimeOrFour x
h : Associated 1 (Multiset.prod g)
⊢ g = 0
case h₁.a
g : Multiset ℤ
hg : ∀ (x : ℤ), x ∈ g → OddPrimeOrFour x
h : Associated 1 (Multiset.prod g)
⊢ ∀ (x : ℤ), ¬x ∈ g