have : a * b ≃ 0 ∨ Nonzero (a * b) := (zero? (a * b)).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 b : ℤ
⊢ sgn (a * b) ≃ sgn a * sgn b
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 b : ℤ
this : a * b ≃ 0 ∨ Nonzero (a * b)
⊢ sgn (a * b) ≃ sgn a * sgn b