apply cases_on (motive := λ y => step n₁ ≃ y → step n₁ + m ≃ y + m)
ℕ : Type
inst✝² : Core ℕ
inst✝¹ : Induction ℕ
inst✝ : Addition 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✝² : Core ℕ
inst✝¹ : Induction ℕ
inst✝ : Addition 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✝² : Core ℕ
inst✝¹ : Induction ℕ
inst✝ : Addition 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