case mpr =>
  intro (_ : sgn (p - q) ≃ 0)
  show p ≃ q
  have : p - q ≃ 0 := sgn_zero.mpr ‹sgn (p - q) ≃ 0›
  have : p ≃ q := sub_eqv_zero_iff_eqv.mp 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 : ℚ
⊢ sgn (p - q) ≃ 0 → p ≃ q
no goals