have h2ndvd : ¬2 ∣ q ^ 2 + 3 * s ^ 2 :=
  by
  rw [← even_iff_two_dvd]
  simp [two_ne_zero, hodd', parity_simps]
q s : ℤ
h3_ndvd_q : ¬3 ∣ q
hspos : s ≠ 0
hcoprime' : IsCoprime s q
hodd' : Even q ↔ ¬Even s
⊢ 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
⊢ IsCoprime (3 ^ 2 * 2 * s) (q ^ 2 + 3 * s ^ 2)