case mpr =>
  intro (_ : sgn (n——m) ≃ 0)
  show n——m ≃ 0
  have : ord_sgn (compare n m) ≃ (0:Difference ℕ) := ‹sgn (n——m) ≃ 0›
  have : ord_sgn (compare n m) ≃ ord_sgn Ordering.eq := this
  have : compare n m = Ordering.eq := ord_sgn_inject this
  have : n ≃ m := Natural.compare_eq.mp this
  have : n——m ≃ 0 := zero_diff_eqv.mpr this
  exact this
ℕ : Type
inst✝ : Natural ℕ
n m : ℕ
⊢ (n——m).sgn ≃ 0 → n——m ≃ 0
no goals