have tri : AA.ExactlyOneOfThree (a ≃ 0) (Positive a) (Negative a) :=
  Signed.trichotomy a
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
a : ℤ
⊢ AA.ExactlyOneOfTwo (a ≃ 0) (Nonzero a)
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
a : ℤ
tri : AA.ExactlyOneOfThree (a ≃ 0) (Positive a) (Negative a)
⊢ AA.ExactlyOneOfTwo (a ≃ 0) (Nonzero a)