have : d ≄ 0 := by
  intro (_ : d ≃ 0)
  show False
  apply ‹n ≄ m›
  show n ≃ m
  calc
    n     ≃ _ := Rel.symm add_zero
    n + 0 ≃ _ := AA.substR (Rel.symm ‹d ≃ 0›)
    n + d ≃ _ := ‹n + d ≃ m›
    m     ≃ _ := Rel.refl
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
left✝ : n ≤ m
right✝ : n ≄ m
d : ℕ
h✝ : n + d ≃ m
⊢ step 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
left✝ : n ≤ m
right✝ : n ≄ m
d : ℕ
h✝ : n + d ≃ m
this : d ≄ 0
⊢ step n ≤ m