4(e)

1. assumption-box-1... p ....
2. ... assumption-box-2.... box ~p (as per hint)
3. ... ~p ........... T, 2.
4. ... "bottom" ............ ~e 1,3. .... end of assumption-box-2
5. ~ box ~p ..... ~i 2-4
6. box ~ box ~p ...... 5 , 5.
7. box diamond p ......... Def. diamond. ..... end of assumtion-box-1
8. p -> box diamond p .................... ->i 1-7

How do we introduce the "definition of diamond" construct? For now this looks an adequate way to justify it, but maybe there's some special notation in the book. Anyone know?

I got pretty much the same answer except I redefined the question, without the box and I stated that diamond is equivalent to ~box~ and I left the end of the answer as is simply because all statements were done b4 the answer was attempted.

Yes, that sounds good. Give the def for diamond before doing anything, and then work purely in terms of box. No real need to give the answer in terms of diamond at the end, then... but if diamond is what's specified, it's probably safer and "more complete" to do so? It's no extra work, really.