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 Th4:
  for x being real-valued FinSequence holds |.x.|^2 = |(x,x)|
proof
  let x be real-valued FinSequence;
A1: 0 <= |(x,x)| by RVSUM_1:119;
  |.x.|^2 = (sqrt Sum sqr x)^2 by EUCLID:def 5
    .= |(x,x)| by A1,SQUARE_1:def 2;
  hence thesis;
end;
