reserve x,y,z for object, X,Y for set,
  i,k,n for Nat,
  p,q,r,s for FinSequence,
  w for FinSequence of NAT,
  f for Function;

theorem
  for T being Tree holds elementary_tree 1 c= ^T
proof
  let T be Tree;
  let x be object;
  assume x in elementary_tree 1;
  then reconsider p = x as Element of elementary_tree 1;
  p = {} or p = <*0*> & {} in T & <*0*>^{} = <*0*>
  by FINSEQ_1:34,TARSKI:def 2,TREES_1:22,51;
  hence thesis by Th60;
end;
