induction a
a : ℕ
⊢ ∀ (b : ℕ), a ≠ 0 → b ≠ 0 → a * b ≠ 0
case zero

⊢ ∀ (b : ℕ), zero ≠ 0 → b ≠ 0 → zero * b ≠ 0

case succ
n✝ : ℕ
n_ih✝ : ∀ (b : ℕ), n✝ ≠ 0 → b ≠ 0 → n✝ * b ≠ 0
⊢ ∀ (b : ℕ), succ n✝ ≠ 0 → b ≠ 0 → succ n✝ * b ≠ 0