rcases hcube with (hcube | hcube | hcube) <;> [(use a), (use b), (use c)] <;> exact hcube
a b c p q : ℤ
hp : p ≠ 0
hcoprime : IsCoprime p q
hodd : Even p ↔ ¬Even q
hcube : 2 * p * (p ^ 2 + 3 * q ^ 2) = a ^ 3 ∨ 2 * p * (p ^ 2 + 3 * q ^ 2) = b ^ 3 ∨ 2 * p * (p ^ 2 + 3 * q ^ 2) = c ^ 3
hgcd : IsCoprime (2 * p) (p ^ 2 + 3 * q ^ 2)
⊢ ∃ r, 2 * p * (p ^ 2 + 3 * q ^ 2) = r ^ 3
no goals