reserve n for Nat;

theorem Th1:
  for f be trivial FinSequence
 holds f is empty or ex x be object st f = <*x*>
proof
  let f be trivial FinSequence;
  assume f is non empty;
  then consider x be object such that
A1: f = {x} by ZFMISC_1:131;
  x in {x} by TARSKI:def 1;
  then consider y,z be object such that
A2: x = [y,z] by A1,RELAT_1:def 1;
A3: 1 in dom f by A1,FINSEQ_5:6;
  take z;
  dom f = {y} by A1,A2,RELAT_1:9;
  then 1 = y by A3,TARSKI:def 1;
  hence thesis by A1,A2,FINSEQ_1:def 5;
end;
