Help with this question please.

[Jack Smith]

Can some one help me with this proof?

Let L be the language of strings over {a,b} recursively defined by the
following set of rules
(i) the string ^ is in L (^ is the null string).
(ii) for every x an element of L the strings bax, baax, bbax, and bbaax are
in L.
(iii) nothing is in L unless the first two rules require it.

Let T be the set of strings over {a,b} such that each string in T is either
empy or starts with b, ends with a, and contains no substring of more than
two repeated characters. Show the L = T.

The proof requires me to use Induction to prove that L is a subset (or
equal) to T. Then it requires me to use induction again to show T is a
subset (or equal) to L. By showing this the proof is complete. But I need
help on how to do the induction. Any help is appreciated. Thanks!