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
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
x✝ : p > q
this✝ : q < p
this : sgn (q - p) ≃ -1
⊢ sgn (p - q) ≃ 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
x✝ : p > q
this✝¹ : q < p
this✝ : sgn (q - p) ≃ -1
this : sgn (p - q) ≃ 1
⊢ sgn (p - q) ≃ 1