Take the 2-minute tour ×  I am trying to prove that:  (uv)R =
vRuR  where R is the reversal of a String defined recursively
as:  aR = a  (wa)R = awR  I think I have the base case right,
but I am having trouble with the inductive step and final proof.
here is what I have:  Base Step  prove for n = 1 where |uv| = 1
(uv)R = uReR = uR = u (where e is the empty string)  I dont
really know where to go from here, any help would be great.
share|improve this question Instead of doing induction over the
entire $|uv|$, let the induction variable be just $|v|$ and keep
the $u$ constant-but-arbitrary throughout the induction proof.
(Also, since $u$ can be empty, the base case should probably be
$|u|=0$ rather than $|u|=1$). –  Henning Makholm Sep 3 '11 at
22:01 add comment  1 Answer  up vote 2 down vote accepted  I
agree with Henning that your induction should be on $|v|$. Note
in the case $|v| = 1$, you're done by definition. It's probably
also worth mentioning something about the empty string for
completeness.  Let