list a is a permutation of list b if any of the following are true: 1) both lists are null, 2) a.head = b.head, and a.tail is a permutation of b.tail, 3) a.head b.head and there exists another list c such that a.tail is a permutation of b.head:c and b.tail is a permutation of a.head:c.

Using a proof by induction, show that this permutation relation is symmetric, i.e., if list a is a permutation of list b, then list b is a permutation of list a.