have : a ≃ 0 ∨ b ≃ 0 := mul_split_zero.mp ‹a * b ≃ 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 b : ℤ
this : a * b ≃ 0 ∨ Nonzero (a * b)
h✝ : a * b ≃ 0
⊢ 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)
h✝ : a * b ≃ 0
this : a ≃ 0 ∨ b ≃ 0
⊢ sgn (a * b) ≃ sgn a * sgn b