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
  T|(<*> NAT) = T
proof
A1: <*> NAT in T by Th21;
  thus T|(<*> NAT) c= T
  proof
    let x be object;
    assume x in T|(<*> NAT);
    then reconsider p = x as Element of T|(<*> NAT);
 {}^p = p by FINSEQ_1:34;
    hence thesis by A1,Def6;
  end;
  let x be object;
  assume x in T;
  then reconsider p = x as Element of T;
 {}^p = p by FINSEQ_1:34;
  hence thesis by A1,Def6;
end;
