
theorem Th24:
  for X be RealUnitarySpace, f be Lipschitzian linear-Functional of X
   holds (BoundedLinearFunctionalsNorm X).f = upper_bound PreNorms f
proof
  let X be RealUnitarySpace;
  let f be Lipschitzian linear-Functional of X;
  reconsider f9=f as set;
  thus (BoundedLinearFunctionalsNorm X).f =
       upper_bound PreNorms(Bound2Lipschitz(f9,X)) by Def14
    .= upper_bound PreNorms f;
end;
