apply ind_on (motive := λ n => n + m ≃ n + k → m ≃ k) n
ℕ : Type
inst✝² : Core ℕ
inst✝¹ : Induction ℕ
inst✝ : Addition ℕ
n m k : ℕ
⊢ n + m ≃ n + k → m ≃ k
case zero
ℕ : Type
inst✝² : Core ℕ
inst✝¹ : Induction ℕ
inst✝ : Addition ℕ
n m k : ℕ
⊢ 0 + m ≃ 0 + k → m ≃ k

case step
ℕ : Type
inst✝² : Core ℕ
inst✝¹ : Induction ℕ
inst✝ : Addition ℕ
n m k : ℕ
⊢ ∀ (m_1 : ℕ), (m_1 + m ≃ m_1 + k → m ≃ k) → step m_1 + m ≃ step m_1 + k → m ≃ k