have : sgn a ≃ -1 := sgn_negative.mp ‹Negative 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
this : AA.OneOfThree (a ≃ 0) (Positive a) (Negative a)
c✝ : Negative a
⊢ sgn (sgn a) ≃ sgn 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
this✝ : AA.OneOfThree (a ≃ 0) (Positive a) (Negative a)
c✝ : Negative a
this : sgn a ≃ -1
⊢ sgn (sgn a) ≃ sgn a