case mpr =>
  intro (_ : sgn (p - q) ≄ -1)
  show p ≥ q
  have : sgn (q - p) ≄ 1 := by
    intro (_ : sgn (q - p) ≃ 1)
    show False
    have : sgn (p - q) ≃ -1 := calc
      sgn (p - q)    ≃ _ := sgn_subst (eqv_symm neg_sub)
      sgn (-(q - p)) ≃ _ := sgn_compat_neg
      (-sgn (q - p)) ≃ _ := AA.subst₁ ‹sgn (q - p) ≃ 1›
      (-1)           ≃ _ := Rel.refl
    exact absurd ‹sgn (p - q) ≃ -1› ‹sgn (p - q) ≄ -1›
  have : q ≤ p := le_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