Give a proof similar to that used for Theorem 14.2 to show that the total number of comparisons required by any series of n or more searches S on a self-organizing list of length n using the count heuristic is never more than twice the total number of comparisons required when series S is applied to the list stored in its optimal static order.

Theorem 14.2 The total number of comparisons required by any series S of n or more searches on a self-organizing list of length n using the move-to-front heuristic is never more than twice the total number of comparisons required when series S is applied to the list stored in its optimal static order.