have ss : k = 0 ∨ 0 < k := Nat.eq_zero_or_pos k
case intro.intro
a b c : ℤθ
n : ℕ
h : 1 ≤ n
k : ℕ
h1 : 3 ^ k ∣ 3 * n
h2 : ¬3 ^ (k + 1) ∣ 3 * n
⊢ ∃ a b, 1 ≤ a ∧ (3 * ↑n = 3 ^ a * (3 * b + 1) ∨ 3 * ↑n = 3 ^ a * (3 * b + 2))
case intro.intro
a b c : ℤθ
n : ℕ
h : 1 ≤ n
k : ℕ
h1 : 3 ^ k ∣ 3 * n
h2 : ¬3 ^ (k + 1) ∣ 3 * n
ss : k = 0 ∨ 0 < k
⊢ ∃ a b, 1 ≤ a ∧ (3 * ↑n = 3 ^ a * (3 * b + 1) ∨ 3 * ↑n = 3 ^ a * (3 * b + 2))