
theorem Th5:
  for X being set, fs being FinSequence of X, fss being Subset of
  fs holds dom Seq fss = dom Sgm (dom fss)
proof
  let X be set, fs be FinSequence of X, fss be Subset of fs;
A1: rng Sgm(dom fss) c= dom fss by FINSEQ_1:def 14;
  Seq fss = fss * Sgm (dom fss) by FINSEQ_1:def 15;
  hence thesis by A1,RELAT_1:27;
end;
