reserve x, y, z for object,
  i, j, n for Nat,
  p, q, r for FinSequence,
  v for FinSequence of NAT;

theorem
  for T being DecoratedTree holds dom (x-tree T) = ^dom T
proof
  let T be DecoratedTree;
   dom (x-tree <*T*>) = tree(doms <*T*>) & doms <*T*> = <*dom T*> by Th10,
FINSEQ_3:132;
  hence thesis by TREES_3:def 16;
end;
