
theorem Th22:
  for X,Y be RealNormSpace holds
  MultilinearOperators(<*X*>,Y) = LinearOperators(product <*X*>,Y)
  proof
    let X,Y be RealNormSpace;

    for f be object holds
    f in MultilinearOperators(<*X*>,Y)
    iff f in LinearOperators(product <*X*>,Y)
    proof
      let f be object;

      f is LinearOperator of product <*X*>,Y
      iff f is MultilinearOperator of <*X*>,Y by Th20;

      hence thesis by LOPBAN_1:def 6,LOPBAN10:def 7;
    end;
    hence thesis by TARSKI:2;
  end;
