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 Th5:
  for x being real-valued FinSequence holds |.x.| = sqrt |(x,x)|
proof
  let x be real-valued FinSequence;
  |.x.| = sqrt |.x.|^2 by EUCLID:9,SQUARE_1:22
    .= sqrt |(x,x)| by Th4;
  hence thesis;
end;
