Consider a constraint on a sequence of variables functionally determining a result variable that is unchanged under reversal of the sequence. Most such constraints have a compact encoding via an automaton augmented with accumulators, but it is unknown how to maintain domain consistency efficiently for most of them. Using such an automaton for such a constraint, we derive an implied constraint between the result variables for a sequence, a prefix thereof, and the corresponding suffix. We show the usefulness of this implied constraint in constraint solving, both by local search and by propagation-based systematic search.