calc
  sgn (a * b)   ≃ _ := sgn_zero.mp ‹a * b ≃ 0›
  0             ≃ _ := Rel.symm AA.absorbR
  sgn a * 0     ≃ _ := AA.substR (Rel.symm (sgn_zero.mp ‹b ≃ 0›))
  sgn a * sgn b ≃ _ := 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 b : ℤ
this✝ : a * b ≃ 0 ∨ Nonzero (a * b)
h✝¹ : a * b ≃ 0
this : a ≃ 0 ∨ b ≃ 0
h✝ : b ≃ 0
⊢ sgn (a * b) ≃ sgn a * sgn b
no goals