case mpr =>
  intro (_ : sgn p ≃ -1)
  show p < 0
  have : sgn (p - 0) ≃ -1 := calc
    _ ≃ sgn (p - 0) := Rel.refl
    _ ≃ sgn p       := sgn_subst sub_zero
    _ ≃ -1          := ‹sgn p ≃ -1›
  have : p < 0 := lt_sgn.mpr this
  exact this
ℕ ℤ ℚ : Type
inst✝¹⁰ : Natural ℕ
inst✝⁹ : Integer ℤ
inst✝⁸ : Core ℚ
inst✝⁷ : Addition ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Negation ℚ
inst✝⁴ : Sign ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Order ℚ
p : ℚ
⊢ sgn p ≃ -1 → p < 0
no goals