theorem Th22:
  |(p1-p2, p3)| = |(p1, p3)| - |(p2, p3)|
proof
  |(p1 - p2, p3)| = |(p1, p3)| + |(-p2, p3)| by Th16
    .= |(p1, p3)| + - |(p2, p3)| by Th19;
  hence thesis;
end;
