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 Th17:
  for x being Real holds |(x*p1, p2)| = x*|(p1, p2)|
proof
  let x be Real;
  reconsider f1=p1,f2=p2 as FinSequence of REAL by EUCLID:24;
  reconsider q1 = p1 as Element of REAL n by EUCLID:22;
  len f1=n & len f2=n by CARD_1:def 7;
  hence thesis by RVSUM_1:121;
end;
