
theorem
  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 .|.(-y) by Th10
  .= - - x .|. y by Th9
  .= x .|. y;
end;
