
theorem Th21:
  for X being RealNormSpace-Sequence,
      Y be RealNormSpace
  for f be MultilinearOperator of X,Y
  st (for x be VECTOR of product X holds f.x = 0.Y)
  holds f is Lipschitzian
  proof
    let X be RealNormSpace-Sequence,
        Y be RealNormSpace;
    let f be MultilinearOperator of X,Y such that
    A1: for x be VECTOR of product X holds f.x=0.Y;
    A2: now
      let x be VECTOR of product X;
      thus ||. f.x .|| = ||. 0.Y .|| by A1
      .= 0 * NrProduct x;
    end;
    take 0;
    thus thesis by A2;
  end;
