reserve
  a,b,c,d,e for Ordinal,
  m,n for Nat,
  f for Ordinal-Sequence,
  x for object;
reserve S,S1,S2 for Sequence;

theorem Th5:
  for f being Sequence holds f is infinite iff omega c= dom f
  proof
    let f be Sequence;
    f is infinite iff dom f is infinite by FINSET_1:10;
    hence thesis by CARD_3:85;
  end;
