∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : UniqueFactorizationMonoid A] {K : Type u_2}
  [inst_3 : Field K] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K] {x y : K},
  IsFractionRing.num A y * ↑(IsFractionRing.den A x) = IsFractionRing.num A x * ↑(IsFractionRing.den A y) ↔ x = y