case mp =>
  intro (_ : p > q)
  show sgn (p - q) ≃ 1
  have : q < p := ‹p > q›
  have : sgn (q - p) ≃ -1 := lt_sgn.mp this
  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))        ≃ _ := Integer.neg_involutive
    1              ≃ _ := Rel.refl
  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
⊢ p > q → sgn (p - q) ≃ 1
no goals