reserve
  X,x,y,z for set,
  k,n,m for Nat ,
  f for Function,
  p,q,r for FinSequence of NAT;
reserve p1,p2,p3 for FinSequence;
reserve T,T1 for Tree;
reserve fT,fT1 for finite Tree;
reserve t for Element of T;
reserve w for FinSequence;
reserve t1,t2 for Element of T;

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;
