apply cases_on (motive := λ x => x * m ≃ 0 → x ≃ 0 ∨ m ≃ 0) n
case mp
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n m : ℕ
⊢ n * m ≃ 0 → n ≃ 0 ∨ m ≃ 0
case mp.zero
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n m : ℕ
⊢ 0 * m ≃ 0 → 0 ≃ 0 ∨ m ≃ 0

case mp.step
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n m : ℕ
⊢ ∀ (m_1 : ℕ), step m_1 * m ≃ 0 → step m_1 ≃ 0 ∨ m ≃ 0