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

theorem Th10:
  for p being DTree-yielding FinSequence holds dom (x-tree(p)) = tree(doms p)
proof
  let p be DTree-yielding FinSequence;
 ex q being DTree-yielding FinSequence st
  p = q & dom (x-tree(p)) = tree(doms q) by Def4;
  hence thesis;
end;
