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 Th26:
  for X be RealNormSpace holds
   0.(R_VectorSpace_of_BoundedLinearFunctionals X) = (the carrier of X) --> 0
proof
  let X be RealNormSpace;
A1: 0.(X*') =(the carrier of X) -->0 by Th22b;
  R_VectorSpace_of_BoundedLinearFunctionals X is Subspace of X*'
  by Th22,RSSPACE:11;
  hence thesis by A1,RLSUB_1:11;
end;
