apply cases_on (motive := λ y => step n₁ ≃ y → step n₁ * m ≃ y * m)
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 n₁ : ℕ
ih : ∀ (y : ℕ), n₁ ≃ y → n₁ * m ≃ y * m
n₂ : ℕ
⊢ step n₁ ≃ n₂ → step 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 n₁ : ℕ
ih : ∀ (y : ℕ), n₁ ≃ y → n₁ * m ≃ y * m
n₂ : ℕ
⊢ step n₁ ≃ 0 → step n₁ * m ≃ 0 * 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 n₁ : ℕ
ih : ∀ (y : ℕ), n₁ ≃ y → n₁ * m ≃ y * m
n₂ : ℕ
⊢ ∀ (m_1 : ℕ), step n₁ ≃ step m_1 → step n₁ * m ≃ step m_1 * m