intro n (ih : n * (m + k) ≃ n * m + n * k)
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 k : ℕ
⊢ ∀ (m_1 : ℕ), m_1 * (m + k) ≃ m_1 * m + m_1 * k → step m_1 * (m + k) ≃ step m_1 * m + step m_1 * k
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 k n : ℕ
ih : n * (m + k) ≃ n * m + n * k
⊢ step n * (m + k) ≃ step n * m + step n * k