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