Hi, apologies for the late reply. The last few days have been a mess so no time for math

The only thing I can come up with is that since

, then

, but that doesn't really prove either (1) nor (2)..

Indeed, that doesn't...but and now you get what you wanted...
I figure that I need to show that

. If I assume that (2) is true, I should be able to take the annihilator of both sides of (2) and get to the wanted result.

Then by (a) I have that

Ah, I find this to be really hard!

Yes, it really requires concentration. Try again, since the last days you did no much math (or at all). Tonio
Thanks!