case mp =>
  intro (_ : Negative (n——m))
  show sgn (n——m) ≃ -1
  have : n < m := neg_diff_lt.mp ‹Negative (n——m)›
  have : compare n m = Ordering.lt := Natural.compare_lt.mpr this
  have : ord_sgn (compare n m) ≃ ord_sgn Ordering.lt :=
    ord_sgn_subst (ℤ := Difference ℕ) this
  have : ord_sgn (compare n m) ≃ (-1:Difference ℕ) := this
  have : sgn (n——m) ≃ -1 := this
  exact this
ℕ : Type
inst✝ : Natural ℕ
n m : ℕ
⊢ Negative (n——m) → (n——m).sgn ≃ -1
no goals