apply ind_on (motive := λ x => x * 0 ≃ 0) n
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 : ℕ
⊢ n * 0 ≃ 0
case 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 : ℕ
⊢ 0 * 0 ≃ 0

case 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 : ℕ
⊢ ∀ (m : ℕ), m * 0 ≃ 0 → step m * 0 ≃ 0