theorem
  height elementary_tree 0 = 0
proof
 now
    thus ex p st p in elementary_tree 0 & len p = 0
    proof
      take <*> NAT;
      thus thesis by Th28,TARSKI:def 1;
    end;
    let p;
    assume p in elementary_tree 0;
    then  p = {} by Th28,TARSKI:def 1;
    hence len p <= 0;
  end;
  hence thesis by Def12;
end;
