
theorem Th12:
  for V being RealNormSpace,
      x be Point of V,
      y,z be Point of DualSp V holds
    x .|. (y-z) = x .|. y - x .|. z
proof
  let V be RealNormSpace,
      x be Point of V,
      y,z be Point of DualSp V;
  thus x .|. (y-z)
    =x .|. y + x .|. (-z) by DUALSP01:29
    .=x .|. y + - x.|. z by Th9
    .=x .|. y - x .|. z;
end;
