reserve x for set,
  t,t1,t2 for DecoratedTree;

theorem
  FixedSubtrees t1 = FixedSubtrees t2 implies t1 = t2
proof
  assume FixedSubtrees t1 = FixedSubtrees t2;
  then [{},t1] in FixedSubtrees t2 by Th15;
  then consider n being Node of t2 such that
A1: [{},t1] = [n,t2|n];
  {} = n & t1 = t2|n by A1,XTUPLE_0:1;
  hence thesis by Th1;
end;
