have abTri
  : AA.ExactlyOneOfThree (a - b ≃ 0) (Positive (a - b)) (Negative (a - b))
  := Signed.trichotomy (a - b)
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
⊢ AA.ExactlyOneOfThree (a < b) (a ≃ b) (a > b)
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
abTri : AA.ExactlyOneOfThree (a - b ≃ 0) (Positive (a - b)) (Negative (a - b))
⊢ AA.ExactlyOneOfThree (a < b) (a ≃ b) (a > b)