apply Multiset.eq_zero_of_forall_not_mem
case empty
g : Multiset ℕ
hg : ∀ x ∈ g, OddPrimeOrFour x
h : 1 = g.prod
⊢ g = 0
case empty.a
g : Multiset ℕ
hg : ∀ x ∈ g, OddPrimeOrFour x
h : 1 = g.prod
⊢ ∀ (x : ℕ), x ∉ g