This about the theory or computation. Please explain it by the steps and explain clearly, do not copy any reference, please.

4. In lecture, we defined the extended transition function . : Q Q recursively in terms of , via: 6"(q, wc) = ("(q, w), c), for all w . and c Using this definition, prove that: "(q, xy) = "(6"(q, x), y), for all x, y . In other words, the state that you get to by starting at q and reading xy, is the state that you get to by starting at q, reading x, then reading y. Hint: Use induction on the length of y. You can follow the examples for induction on strings from Erickson's notes section 1. However, in this case you should do induction by adding a character to the end of y (not beginning of y as in the Erickson examples). This makes things match the recursive definition * better