reserve x,y,x1,x2,z for set,
  n,m,k for Nat,
  t1 for (DecoratedTree of [: NAT,NAT :]),
  w,s,t,u for FinSequence of NAT,
  D for non empty set;

theorem Th3:
  for Z being Tree,n,m st n <= m & <*m*> in Z holds <*n*> in Z
proof
  reconsider s = {} as FinSequence of NAT by TREES_1:22;
  let Z be Tree,n,m;
  assume that
A1: n <= m and
A2: <*m*> in Z;
  {}^<*m*> in Z by A2,FINSEQ_1:34;
  then s^<*n*> in Z by A1,TREES_1:def 3;
  hence thesis by FINSEQ_1:34;
end;
