apply ind_on (motive := λ x => ∀ y, x ≃ y → x * m ≃ y * m) n₁
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
n₁ n₂ m : ℕ
⊢ n₁ ≃ n₂ → n₁ * m ≃ n₂ * m
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
n₁ n₂ m : ℕ
⊢ ∀ (y : ℕ), 0 ≃ y → 0 * m ≃ y * m

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
n₁ n₂ m : ℕ
⊢ ∀ (m_1 : ℕ), (∀ (y : ℕ), m_1 ≃ y → m_1 * m ≃ y * m) → ∀ (y : ℕ), step m_1 ≃ y → step m_1 * m ≃ y * m