Hello TulkiWe do the first part by Induction. The second is immediately obvious. I'm using the notation to denote .

First we prove the Lemma:

Proof of Lemma:

, using the fact that and

Then the Induction Hypothesis: Suppose is the propositional function: For any

Then, using the above Lemma:

So .

Now is self-evident.

So the result is proved, by Induction, for all

For the second part, we note that for all , and the result follows immediately.

Grandad