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 T1,T2 being Tree holds elementary_tree 2 c= tree(T1,T2)
proof
  let T1,T2 be Tree;
  let x be object;
  assume x in elementary_tree 2;
  then reconsider p = x as Element of elementary_tree 2;
  p = {} or p = <*0*> & {} in T1 & <*0*>^{} = <*0*> or
  p = <*1*> & {} in T2 & <*1*>^{} = <*1*>
  by ENUMSET1:def 1,FINSEQ_1:34,TREES_1:22,53;
  hence thesis by Th68;
end;
