rw [MulZeroClass.mul_zero]
case h.h
a b c : ℤθ
⊢ Nat.zero = 3 * 0

case succ
a b c : ℤθ
k : ℕ
hk : ∃ a, k = 3 * a ∨ k = 3 * a + 1 ∨ k = 3 * a + 2
⊢ ∃ a, Nat.succ k = 3 * a ∨ Nat.succ k = 3 * a + 1 ∨ Nat.succ k = 3 * a + 2
case h.h
a b c : ℤθ
⊢ Nat.zero = 0

case succ
a b c : ℤθ
k : ℕ
hk : ∃ a, k = 3 * a ∨ k = 3 * a + 1 ∨ k = 3 * a + 2
⊢ ∃ a, Nat.succ k = 3 * a ∨ Nat.succ k = 3 * a + 1 ∨ Nat.succ k = 3 * a + 2