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 Th37:
  dom (T*(t succ)) = dom (t succ)
proof
  rng (t succ) c= dom T;
  hence thesis by RELAT_1:27;
end;
