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
x✝ : -ε ≤ q - p
⊢ p - ε ≤ q
no goals