Somehow different question about a proof

Hello,

i'm reading the book functional analysis by rudin. And there is a theorem 8.5 on page 213-215(about fundamental solutions).

He uses the lemma 8.3 within this proof, but i can't see where he uses the thm. 8.4? Does he uses this thm?? I think he don't.

But on the other side, i'm confused by the fact that he put theorem 8.4 between 8.3 and 8.5.

I coundn't find a link to the book, but maybe someone has the possibility to take a look at the proof 8.5 and tell me his opinion.

Regards