reserve x for set,
  t,t1,t2 for DecoratedTree;
reserve C for set;
reserve X,Y for non empty constituted-DTrees set;

theorem
  t in X implies t in Subtrees X
proof
  assume t in X;
  then reconsider t as Element of X;
  reconsider e = {} as Node of t by TREES_1:22;
  t|e = t by Th1;
  hence thesis;
end;
