calc
  _ ≃ r * p := eqv_refl
  _ ≃ p * r := mul_comm
  _ < q * r := lt_substL_mul_pos ‹r > 0› ‹p < q›
  _ ≃ r * q := mul_comm
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 r : ℚ
x✝¹ : r > 0
x✝ : p < q
⊢ r * p < r * q
no goals