case mpr =>
  intro (_ : sgn (p - q) ≃ 1)
  show p > q
  have : sgn (q - p) ≃ -1 := calc
    sgn (q - p)    ≃ _ := sgn_subst (eqv_symm neg_sub)
    sgn (-(p - q)) ≃ _ := sgn_compat_neg
    (-sgn (p - q)) ≃ _ := AA.subst₁ ‹sgn (p - q) ≃ 1›
    (-1)           ≃ _ := Rel.refl
  have : q < p := lt_sgn.mpr this
  have : p > q := 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) ≃ 1 → p > q
no goals