{H : Type u} →
  [inst : NormedAddCommGroup H] →
    [inst_1 : InnerProductSpace ℂ H] →
      [inst_2 : CompleteSpace H] →
        (carrier : Set (H →L[ℂ] H)) →
          (∀ {a b : H →L[ℂ] H}, a ∈ carrier → b ∈ carrier → a * b ∈ carrier) →
            1 ∈ carrier →
              (∀ {a b : H →L[ℂ] H}, a ∈ carrier → b ∈ carrier → a + b ∈ carrier) →
                0 ∈ carrier →
                  (∀ (r : ℂ), (algebraMap ℂ (H →L[ℂ] H)) r ∈ carrier) →
                    (∀ {a : H →L[ℂ] H}, a ∈ carrier → star a ∈ carrier) →
                      carrier.centralizer.centralizer = carrier → VonNeumannAlgebra H