apply And.intro
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)
case left
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)
⊢ a ≃ 0 ∨ Nonzero a

case right
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)
⊢ ¬(a ≃ 0 ∧ Nonzero a)