reserve x for set,
  t,t1,t2 for DecoratedTree;
reserve C for set;
reserve X,Y for non empty constituted-DTrees set;
reserve T for DecoratedTree,
  p for FinSequence of NAT;
reserve T for finite-branching DecoratedTree,
  t for Element of dom T,
  x for FinSequence,
  n, m for Nat;

theorem Th38:
  dom succ(T,t) = dom (t succ)
proof
  thus dom succ(T,t) = dom (T*(t succ)) by Th36
    .= dom (t succ) by Th37;
end;
