calc
  _ ≃ q              := eqv_refl
  _ ≃ q + 0          := eqv_symm add_identR
  _ ≃ q + ((-p) + p) := add_substR (eqv_symm add_inverseL)
  _ ≃ (q + (-p)) + p := eqv_symm add_assoc
  _ ≃ (q - p) + p    := add_substL (eqv_symm sub_add_neg)
  _ ≤ ε + p          := le_substL_add ‹q - p ≤ ε›
  _ ≃ p + ε          := add_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
ε p q : ℚ
x✝ : q - p ≤ ε
⊢ q ≤ p + ε
no goals