∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
  {x y : α},
  x ≠ 0 →
    y ≠ 0 → (x ∣ y) = (UniqueFactorizationMonoid.normalizedFactors x ≤ UniqueFactorizationMonoid.normalizedFactors y)