∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
  {a b : M},
  UniqueFactorizationMonoid.primeFactors a = UniqueFactorizationMonoid.primeFactors b →
    UniqueFactorizationMonoid.radical a = UniqueFactorizationMonoid.radical b