have : sgn p ≃ 0 ∨ sgn q ≃ 0 := Integer.mul_split_zero.mp this
ℕ ℤ ℚ : Type
inst✝⁹ : Natural ℕ
inst✝⁸ : Integer ℤ
inst✝⁷ : Core ℚ
inst✝⁶ : Addition ℚ
inst✝⁵ : Multiplication ℚ
inst✝⁴ : Negation ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Sign ℚ
p q : ℚ
x✝ : p * q ≃ 0
this : sgn p * sgn q ≃ 0
⊢ p ≃ 0 ∨ q ≃ 0
ℕ ℤ ℚ : Type
inst✝⁹ : Natural ℕ
inst✝⁸ : Integer ℤ
inst✝⁷ : Core ℚ
inst✝⁶ : Addition ℚ
inst✝⁵ : Multiplication ℚ
inst✝⁴ : Negation ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Sign ℚ
p q : ℚ
x✝ : p * q ≃ 0
this✝ : sgn p * sgn q ≃ 0
this : sgn p ≃ 0 ∨ sgn q ≃ 0
⊢ p ≃ 0 ∨ q ≃ 0