have : sgn a ≃ sgn b := positive_mul_iff_sgn_eqv.mp ‹Positive (a * 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✝¹ : Nonzero (a * b)
left✝ : Sqrt1 (sgn a)
right✝ : Sqrt1 (sgn b)
this : Positive (a * b) ∨ Negative (a * b)
h✝ : Positive (a * b)
⊢ 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✝¹ : a * b ≃ 0 ∨ Nonzero (a * b)
h✝¹ : Nonzero (a * b)
left✝ : Sqrt1 (sgn a)
right✝ : Sqrt1 (sgn b)
this✝ : Positive (a * b) ∨ Negative (a * b)
h✝ : Positive (a * b)
this : sgn a ≃ sgn b
⊢ sgn (a * b) ≃ sgn a * sgn b