calc
  sgn (sgn a)  ≃ _ := sgn_subst ‹sgn a ≃ -1›
  sgn (-1 : ℤ) ≃ _ := sgn_negative.mp neg_one_negative
  (-1)         ≃ _ := Rel.symm ‹sgn a ≃ -1›
  sgn a        ≃ _ := Rel.refl
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
no goals