The ``value equivalence'' defined for tuples could be extended to consider histories. However, such an extension would be rather inappropriate (+E1): value equivalence concerns attribute values and completely disregards time, whereas history equivalence implies a common evolution along with time (implicitly assumes equality of timestamps prior to compare data values). The extension would violate the rationale of the introduction of history-oriented models.
``History equivalent'' is a concept closer to ``snapshot equivalent'' (-E3) rather than to ``value equivalent'' (+E5). Anyway, ``history equivalent'' seems to be more general and intuitive (+E8). An alternative definition could be: ``Two objects are history equivalent if their histories are shapshot equivalent.