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 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;
