simp only [Multiset.not_mem_zero, IsEmpty.forall_iff, forall_const, Multiset.prod_zero,
  true_and]
case h
R : Type u_1
inst✝ : CommMonoidWithZero R
l : Multiset R
⊢ (∀ b ∈ 0, Prime b) ∧ Associated (Multiset.prod 0) 1
case h
R : Type u_1
inst✝ : CommMonoidWithZero R
l : Multiset R
⊢ Associated 1 1