obtain ⟨c, hc⟩ := _root_.factors a x hcoprime hodd hfactor
case inr.intro
a : ℤ√(-3)
x : ℤ
hcoprime : IsCoprime a.re a.im
hfactor : x ∣ a.norm
hprime : x.natAbs.Prime
hodd : Odd x
⊢ ∃ c, |x| = c.norm ∧ 0 ≤ c.re ∧ c.im ≠ 0
case inr.intro.intro
a : ℤ√(-3)
x : ℤ
hcoprime : IsCoprime a.re a.im
hfactor : x ∣ a.norm
hprime : x.natAbs.Prime
hodd : Odd x
c : ℤ√(-3)
hc : |x| = c.norm
⊢ ∃ c, |x| = c.norm ∧ 0 ≤ c.re ∧ c.im ≠ 0