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