apply cases_on (motive := λ d => n + d ≃ m → n < m ∨ n ≃ m) d
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
x✝ : n ≤ m
d : ℕ
⊢ n + d ≃ m → n < m ∨ n ≃ m
case zero
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
x✝ : n ≤ m
d : ℕ
⊢ n + 0 ≃ m → n < m ∨ n ≃ m

case step
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
x✝ : n ≤ m
d : ℕ
⊢ ∀ (m_1 : ℕ), n + step m_1 ≃ m → n < m ∨ n ≃ m