have : n + step d ≃ m := calc
  n + step d   ≃ _ := add_step
  step (n + d) ≃ _ := Rel.symm step_add
  step n + d   ≃ _ := ‹step n + d ≃ m›
  m            ≃ _ := Rel.refl
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
x✝ : step n ≤ m
d : ℕ
h✝ : step n + d ≃ m
⊢ 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 : ℕ
x✝ : step n ≤ m
d : ℕ
h✝ : step n + d ≃ m
this : n + step d ≃ m
⊢ n < m