
theorem Th10:
  for X,Y be RealLinearSpace holds
  MultilinearOperators(<*X*>,Y) = LinearOperators(product <*X*>,Y)
  proof
    let X,Y be RealLinearSpace;
    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 Th9;
      hence thesis by LOPBAN_1:def 6,LOPBAN10:def 4;
    end;
    hence thesis by TARSKI:2;
  end;
