have : step n ≤ m := lt_step_le.mp ‹n < m›
case mp
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
⊢ ∃ k, Positive k ∧ m ≃ n + k
case mp
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
this : step n ≤ m
⊢ ∃ k, Positive k ∧ m ≃ n + k