reserve V for non empty RealLinearSpace;
reserve S for Real_Sequence;
reserve k,n,m,m1 for Nat;
reserve g,h,r,x for Real;

theorem Th43:
  for X be RealNormSpace holds DualSp X is RealBanachSpace
proof
  let X be RealNormSpace;
  for seq be sequence of DualSp X st seq
  is Cauchy_sequence_by_Norm holds seq is convergent by Th42;
  hence thesis by LOPBAN_1:def 15;
end;
