reserve x,z for set;
reserve k for Element of NAT;
reserve D for non empty set;
reserve X for set;
reserve p,r for relation;
reserve a,a1,a2,b for FinSequence;
reserve a,b for FinSequence of D;
reserve p,r for Element of relations_on D;

theorem
  {a} is Element of relations_on D
proof
A1: for a1,a2 being FinSequence of D st a1 in {a} & a2 in {a} holds len a1 =
  len a2
  proof
    let a1,a2 be FinSequence of D;
    assume that
A2: a1 in {a} and
A3: a2 in {a};
    a1 = a by A2,TARSKI:def 1;
    hence thesis by A3,TARSKI:def 1;
  end;
  a in D* by FINSEQ_1:def 11;
  then {a} c= D* by ZFMISC_1:31;
  hence thesis by A1,Def7;
end;
