case mpr =>
  intro (_ : q ≤ p + ε)
  show q - p ≤ ε
  calc
    _ ≃ q - p          := eqv_refl
    _ ≃ q + (-p)       := sub_add_neg
    _ ≤ (p + ε) + (-p) := le_substL_add ‹q ≤ p+ε›
    _ ≃ (ε + p) + (-p) := add_substL add_comm
    _ ≃ ε + (p + (-p)) := add_assoc
    _ ≃ ε + 0          := add_substR add_inverseR
    _ ≃ ε              := add_identR
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
ε p q : ℚ
⊢ q ≤ p + ε → q - p ≤ ε
no goals