Question

The reversal of a string w, denoted w^R, is the string "spelled backwards". For example (reverse)^R = esrever. A careful definition can be given by induction on the length of
a string:

1. If w is a string of length 0, then w^R = epsilon
2. If w = ua, where a is an element of all alphabet and u is an element of (alphabet)*, is a string of length n+1>0, then w^R = au^R/

Prove the following by induction
(w^R)^R = w