reserve i, n for Nat,
  x, y, a for Real,
  v for Element of n-tuples_on REAL,
  p, p1, p2, p3, q, q1, q2 for Point of TOP-REAL n;

theorem Th29:
  |(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 Th27
    .= |(p,p)| - 2*|(p,q)| + |(q, q)|;
  hence thesis;
end;
