
theorem Th2:
  for X being set, fs being FinSequence of X, fss being Subset of fs holds
    len (Seq fss) <= len fs
proof
  let X be set, fs be FinSequence of X, fss be Subset of fs;
A1: Seq fss = fss * Sgm(dom fss) by FINSEQ_1:def 15;
  rng (Sgm(dom fss)) = dom fss by FINSEQ_1:def 14;
  then len (Seq fss) = len Sgm (dom fss) by A1,FINSEQ_2:29
    .= card (dom fss) by FINSEQ_3:39
    .= card fss by CARD_1:62;
  hence thesis by NAT_1:43;
end;
