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;

theorem Th28:
  elementary_tree 0 = { {} }
proof
 now
    set x = the Element of { <*j*> where j is Nat : j < 0 };
    assume { <*j*> where j is Nat : j < 0 } <> {};
then  x in { <*j*> where j is Nat : j < 0 };
then  ex k st x = <*k*> & k < 0;
    hence contradiction;
  end;
  hence thesis;
end;
