case mp =>
  intro (_ : p ≥ q) (_ : sgn (p - q) ≃ -1)
  show False
  have : q ≤ p := ‹p ≥ q›
  have : sgn (q - p) ≄ 1 := le_sgn.mp this
  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))        ≃ _ := Integer.neg_involutive
    1              ≃ _ := Rel.refl
  exact absurd ‹sgn (q - p) ≃ 1› ‹sgn (q - p) ≄ 1›
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
⊢ p ≥ q → sgn (p - q) ≄ -1
no goals