case mpr =>
  intro (_ : sgn (a - b) ≃ -1)
  show a < b
  have : Negative (a - b) := sgn_negative.mpr ‹sgn (a - b) ≃ -1›
  have : a < b := lt_iff_neg_diff.mpr this
  exact this
ℕ : Type
inst✝⁷ : Natural ℕ
ℤ : Type
inst✝⁶ : Core ℤ
inst✝⁵ : Addition ℤ
inst✝⁴ : Multiplication ℤ
inst✝³ : Negation ℤ
inst✝² : Subtraction ℤ
inst✝¹ : Sign ℤ
inst✝ : Order ℤ
a b : ℤ
⊢ sgn (a - b) ≃ -1 → a < b
no goals