
theorem Th2:
  for V being RealNormSpace,
      x be Point of V,
      y be Point of DualSp V holds
     |. x.|.y .| <= ||.y.|| * ||.x.||
proof
  let V be RealNormSpace;
  let x be Point of V;
  let y be Point of DualSp V;
  reconsider y0=y as Lipschitzian linear-Functional of V
    by DUALSP01:def 10;
  |.y0.x.| <= ||.y.|| * ||.x.|| by DUALSP01:26;
  hence thesis;
end;
