have h3ndvd : ¬3 ∣ q ^ 2 + 3 * s ^ 2 := by
  intro H
  apply h3_ndvd_q
  rw [dvd_add_left (dvd_mul_right _ _)] at H
  exact Prime.dvd_of_dvd_pow Int.prime_three H
q s : ℤ
h3_ndvd_q : ¬3 ∣ q
hspos : s ≠ 0
hcoprime' : IsCoprime s q
hodd' : Even q ↔ ¬Even s
h2ndvd : ¬2 ∣ q ^ 2 + 3 * s ^ 2
⊢ IsCoprime (3 ^ 2 * 2 * s) (q ^ 2 + 3 * s ^ 2)
q s : ℤ
h3_ndvd_q : ¬3 ∣ q
hspos : s ≠ 0
hcoprime' : IsCoprime s q
hodd' : Even q ↔ ¬Even s
h2ndvd : ¬2 ∣ q ^ 2 + 3 * s ^ 2
h3ndvd : ¬3 ∣ q ^ 2 + 3 * s ^ 2
⊢ IsCoprime (3 ^ 2 * 2 * s) (q ^ 2 + 3 * s ^ 2)