
theorem Th9:
  for V being RealNormSpace,
      x be Point of V,
      y be Point of DualSp V holds
    x .|. (-y) = - x .|. y
proof
  let V be RealNormSpace,
      x be Point of V,
      y be Point of DualSp V;
  thus x .|. (-y) = x .|. ((-1)*y) by RLVECT_1:16
  .= (-1) * x .|. y by DUALSP01:30
  .= - x .|. y;
end;
