set f := factorization' hcoprime with hf
case intro
a : ℤ√(-3)
r : ℕ
hcoprime : IsCoprime a.re a.im
hcube : r ^ 3 = a.norm.natAbs
h1 : a = (factorization' hcoprime).prod ∨ a = -(factorization' hcoprime).prod
h2 : ∀ pq ∈ factorization' hcoprime, 0 ≤ pq.re ∧ pq.im ≠ 0 ∧ OddPrimeOrFour pq.norm.natAbs
⊢ ∃ g, factorization' hcoprime = 3 • g
case intro
a : ℤ√(-3)
r : ℕ
hcoprime : IsCoprime a.re a.im
hcube : r ^ 3 = a.norm.natAbs
f : Multiset (ℤ√(-3)) := factorization' hcoprime
h1 : a = f.prod ∨ a = -f.prod
h2 : ∀ pq ∈ f, 0 ≤ pq.re ∧ pq.im ≠ 0 ∧ OddPrimeOrFour pq.norm.natAbs
hf : f = factorization' hcoprime
⊢ ∃ g, f = 3 • g