calc
  _ ≃ -ε              := eqv_refl
  _ ≃ 0 + (-ε)        := eqv_symm add_identL
  _ ≃ (-p + p) + (-ε) := add_substL (eqv_symm add_inverseL)
  _ ≃ -p + (p + (-ε)) := add_assoc
  _ ≃ -p + (p - ε)    := add_substR (eqv_symm sub_add_neg)
  _ ≤ -p + q          := le_substR_add ‹p-ε ≤ q›
  _ ≃ q + (-p)        := add_comm
  _ ≃ q - p           := eqv_symm sub_add_neg
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✝ : p - ε ≤ q
⊢ -ε ≤ q - p
no goals