theorem Th139:
  |(p-q, p-q)| = |(p, p)| - 2*|(p, q)| + |(q, q)|
proof
  |(p-q, p-q)| = |(p,p)| - |(p,q)| - |(p,q)| + |(q, q)| by Th137
    .= |(p,p)| - 2*|(p,q)| + |(q, q)|;
  hence thesis;
end;
