reserve X,x for set;

theorem Th4:
  for X for f being FinSequence of X st f <> {} ex g being
  FinSequence of X, d being Element of X st f = g^<*d*>
proof
  let X be set, f be FinSequence of X;
  assume f <> {};
  then consider q being FinSequence, x being object such that
A1: f = q^<*x*> by FINSEQ_1:46;
  reconsider q as FinSequence of X by A1,FINSEQ_1:36;
  take q;
   <*x*> is FinSequence of X by A1,FINSEQ_1:36;
   then reconsider x as Element of X by Th3;
  take x;
  thus thesis by A1;
end;
