reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem
  {}* = {{}}
proof
  thus {}* c= {{}}
  proof
    let x be object;
    assume x in {}*;
    then reconsider f = x as FinSequence of {} by FINSEQ_1:def 11;
    now
      assume x <> {};
      then ex x st x in dom f;
      hence contradiction;
    end;
    hence thesis by ZFMISC_1:31;
  end;
  let x be object;
  assume x in {{}};
  then
A1: x = {} by TARSKI:def 1;
  rng {} = {};
  then x is FinSequence of {} by A1,FINSEQ_1:def 4;
  hence thesis by FINSEQ_1:def 11;
end;
