case mp =>
  intro (_ : Negative (a * b)) (_ : sgn a ≃ sgn b)
  show False
  have : Positive (a * b) := positive_mul_iff_sgn_eqv.mpr ‹sgn a ≃ sgn b›
  have both : Positive (a * b) ∧ Negative (a * b) :=
    And.intro this ‹Negative (a * b)›
  have not_both : ¬(Positive (a * b) ∧ Negative (a * b)) :=
    not_positive_and_negative
  exact absurd both not_both
ℕ : Type
inst✝⁶ : Natural ℕ
ℤ : Type
inst✝⁵ : Core ℤ
inst✝⁴ : Addition ℤ
inst✝³ : Multiplication ℤ
inst✝² : Negation ℤ
inst✝¹ : Sign ℤ
a b : ℤ
inst✝ : Nonzero (a * b)
⊢ Negative (a * b) → sgn a ≄ sgn b
no goals