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