have : -a - -b ≃ b - a := calc
  (-a) - -b    ≃ _ := sub_defn
  (-a) + -(-b) ≃ _ := AA.substR neg_involutive
  (-a) + b     ≃ _ := AA.comm
  b + -a       ≃ _ := Rel.symm sub_defn
  b - a        ≃ _ := Rel.refl
ℕ : Type
inst✝⁷ : Natural ℕ
ℤ : Type
inst✝⁶ : Core ℤ
inst✝⁵ : Addition ℤ
inst✝⁴ : Multiplication ℤ
inst✝³ : Negation ℤ
inst✝² : Subtraction ℤ
inst✝¹ : Sign ℤ
inst✝ : Order ℤ
a b : ℤ
⊢ a < b ↔ -b < -a
ℕ : Type
inst✝⁷ : Natural ℕ
ℤ : Type
inst✝⁶ : Core ℤ
inst✝⁵ : Addition ℤ
inst✝⁴ : Multiplication ℤ
inst✝³ : Negation ℤ
inst✝² : Subtraction ℤ
inst✝¹ : Sign ℤ
inst✝ : Order ℤ
a b : ℤ
this : -a - -b ≃ b - a
⊢ a < b ↔ -b < -a