reserve X for set;
reserve UN for Universe;

theorem
  for X being set for S being Sequence st S = sequence_univers X holds
  last S = {} & S.NAT = {}
  proof
    let X be set;
    let S be Sequence;
    assume
A1: S = sequence_univers X;
    dom sequence_univers X = NAT by Def9;
    hence thesis by A1,Th91;
  end;
