intro ⟨k, (_ : Positive k), (_ : m ≃ n + k)⟩
case mpr
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m : ℕ
⊢ (∃ k, Positive k ∧ m ≃ n + k) → n < m
case mpr
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m k : ℕ
left✝ : Positive k
right✝ : m ≃ n + k
⊢ n < m