theorem Th39:
  for X be RealNormSpace holds DualSp X is RealNormSpace
proof
  let X be RealNormSpace;
  RLSStruct (# BoundedLinearFunctionals X,
   Zero_(BoundedLinearFunctionals X, X*'),
   Add_(BoundedLinearFunctionals X, X*'),
   Mult_(BoundedLinearFunctionals X, X*') #) is RealLinearSpace;
  hence thesis by RSSPACE3:2;
end;
