obtain ⟨ψ, hψ⟩ := ih
case succ
a b c : ℤθ
n : ℕ
ih : ∃ φ, ↑(unit ^ 3 ^ (n + 1)) = 1 + 3 ^ (n + 1) * φ
⊢ ∃ φ, ↑(unit ^ 3 ^ (Nat.succ n + 1)) = 1 + 3 ^ (Nat.succ n + 1) * φ
case succ.intro
a b c : ℤθ
n : ℕ
ψ : ℤθ
hψ : ↑(unit ^ 3 ^ (n + 1)) = 1 + 3 ^ (n + 1) * ψ
⊢ ∃ φ, ↑(unit ^ 3 ^ (Nat.succ n + 1)) = 1 + 3 ^ (Nat.succ n + 1) * φ