case mp =>
  intro (_ : -ε ≤ q - p)
  show p - ε ≤ q
  calc
    _ ≃ p - ε          := eqv_refl
    _ ≃ p + (-ε)       := sub_add_neg
    _ ≤ p + (q - p)    := le_substR_add ‹-ε ≤ q - p›
    _ ≃ p + (q + (-p)) := add_substR sub_add_neg
    _ ≃ p + ((-p) + q) := add_substR add_comm
    _ ≃ (p + (-p)) + q := eqv_symm add_assoc
    _ ≃ 0 + q          := add_substL add_inverseR
    _ ≃ q              := add_identL
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
⊢ -ε ≤ q - p → p - ε ≤ q
no goals