have : sgn (q/r - p/r) ≃ sgn (p - q) := sgn_sub_cancelR_div_neg
ℕ ℤ ℚ : Type
inst✝¹¹ : Natural ℕ
inst✝¹⁰ : Integer ℤ
inst✝⁹ : Core ℚ
inst✝⁸ : Addition ℚ
inst✝⁷ : Multiplication ℚ
inst✝⁶ : Negation ℚ
inst✝⁵ : Sign ℚ
inst✝⁴ : Subtraction ℚ
inst✝³ : Reciprocation ℚ
inst✝² : Division ℚ
inst✝¹ : Order ℚ
p q r : ℚ
inst✝ : AP (sgn r ≃ -1)
x✝ : p < q
this : sgn (p - q) ≃ -1
⊢ q / r < p / r
ℕ ℤ ℚ : Type
inst✝¹¹ : Natural ℕ
inst✝¹⁰ : Integer ℤ
inst✝⁹ : Core ℚ
inst✝⁸ : Addition ℚ
inst✝⁷ : Multiplication ℚ
inst✝⁶ : Negation ℚ
inst✝⁵ : Sign ℚ
inst✝⁴ : Subtraction ℚ
inst✝³ : Reciprocation ℚ
inst✝² : Division ℚ
inst✝¹ : Order ℚ
p q r : ℚ
inst✝ : AP (sgn r ≃ -1)
x✝ : p < q
this✝ : sgn (p - q) ≃ -1
this : sgn (q / r - p / r) ≃ sgn (p - q)
⊢ q / r < p / r