theorem
  height fT = 0 implies fT = elementary_tree 0
proof
  assume
A1: height fT = 0;
  thus fT c= elementary_tree 0
  proof
    let x be object;
    assume x in fT;
    then reconsider t = x as Element of fT;
 len t = 0 by A1,Def12;
then  x = {};
    hence thesis by Th21;
  end;
  let x be object;
  assume x in elementary_tree 0;
then  x = {} by Th28,TARSKI:def 1;
  hence thesis by Th21;
end;
