have : sgn a ≃ 0 := sgn_zero.mp ‹a ≃ 0›
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)
a✝ : a ≃ 0
⊢ 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)
a✝ : a ≃ 0
this : sgn a ≃ 0
⊢ sgn (sgn a) ≃ sgn a