
theorem Th13:
  for V being RealNormSpace,
      y,z be Point of V,
      x be Point of DualSp V holds
   (y-z) .|. x = y .|. x - z .|. x
proof
  let V be RealNormSpace,
      y,z be Point of V,
      x be Point of DualSp V;
  thus (y-z) .|. x = y.|.x + (-z) .|. x by Th5
  .=y .|. x + - z.|. x by Th10
  .=y .|. x - z .|. x;
end;
