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 Th16:
  |(p1 + p2, p3)| = |(p1, p3)| + |(p2, p3)|
proof
  reconsider f1=p1, f2=p2, f3=p3 as FinSequence of REAL by EUCLID:24;
  reconsider q1 = p1, q2=p2 as Element of REAL n by EUCLID:22;
  len f2=n by CARD_1:def 7;
  then
A1: len f1=len f2 & len f2=len f3 by CARD_1:def 7;
  thus thesis by A1,RVSUM_1:120;
end;
