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