
theorem Th26:
  for X be non empty set for Y be RealBanachSpace holds
  R_NormSpace_of_BoundedFunctions(X,Y) is RealBanachSpace
proof
  let X be non empty set;
  let Y be RealBanachSpace;
  for seq be sequence of R_NormSpace_of_BoundedFunctions(X,Y) st seq is
  Cauchy_sequence_by_Norm holds seq is convergent by Th25;
  hence thesis by LOPBAN_1:def 15;
end;
