
theorem Th21X:
  for X be RealUnitarySpace, F be linear-Functional of X
    st F = (the carrier of X) --> 0
  holds F is Lipschitzian
proof
  let X be RealUnitarySpace,
      F be linear-Functional of X;
  assume F = (the carrier of X) --> 0; then
  for x be VECTOR of X holds F.x = 0;
  hence thesis by Th16;
end;
