induction' hx' : x.natAbs using Nat.strong_induction_on with x' IH generalizing a x
a : ℤ√(-3)
x : ℤ
hcoprime : IsCoprime a.re a.im
hodd : Odd x
hfactor : x ∣ a.norm
⊢ ∃ c, |x| = c.norm
case h
x' : ℕ
IH : ∀ m < x', ∀ (a : ℤ√(-3)) (x : ℤ), IsCoprime a.re a.im → Odd x → x ∣ a.norm → x.natAbs = m → ∃ c, |x| = c.norm
a : ℤ√(-3)
x : ℤ
hcoprime : IsCoprime a.re a.im
hodd : Odd x
hfactor : x ∣ a.norm
hx' : x.natAbs = x'
⊢ ∃ c, |x| = c.norm