
theorem Th43:
  for X,Y be RealNormSpace, Z be RealBanachSpace
  holds R_NormSpace_of_BoundedBilinearOperators(X,Y,Z) is RealBanachSpace
  proof
    let X,Y be RealNormSpace;
    let Z be RealBanachSpace;
    for seq be sequence of R_NormSpace_of_BoundedBilinearOperators(X,Y,Z)
    st seq is Cauchy_sequence_by_Norm
    holds seq is convergent by Th42;
    hence thesis by LOPBAN_1:def 15;
  end;
