have : ord_sgn (compare n m) ≃ ord_sgn Ordering.eq :=
  ord_sgn_subst (ℤ := Difference ℕ) this
ℕ : Type
inst✝ : Natural ℕ
n m : ℕ
x✝ : n——m ≃ 0
this✝ : n ≃ m
this : compare n m = Ordering.eq
⊢ (n——m).sgn ≃ 0
ℕ : Type
inst✝ : Natural ℕ
n m : ℕ
x✝ : n——m ≃ 0
this✝¹ : n ≃ m
this✝ : compare n m = Ordering.eq
this : ord_sgn (compare n m) ≃ ord_sgn Ordering.eq
⊢ (n——m).sgn ≃ 0