theorem Th131:
  for x being Real holds |(x*p1, p2)| = x*|(p1, p2)|
proof
  let x be Real;
  reconsider f1=p1,f2=p2 as real-valued FinSequence;
  len f1=n & len f2=n by CARD_1:def 7;
  hence thesis by Th121;
end;
