{α : Type u_2} →
  [inst : CommMonoidWithZero α] →
    [toNormalizationMonoid : NormalizationMonoid α] →
      [toGCDMonoid : GCDMonoid α] →
        (∀ (a b : α), normalize (gcd a b) = gcd a b) →
          (∀ (a b : α), normalize (lcm a b) = lcm a b) → NormalizedGCDMonoid α