Math & Science ⇒ Stylistic Question about Lemma Formatting

[SpacedOut]

I'm currently writing a math paper, and right now I have the following setup

6 part lemma (statement with no proof)
Theorem
proof of theorem
proof of 6 part lemma

My question is how should I format the proof of the 6 part lemma, usually I have been using
\begin{lemma}
Statement of lemma
\end{lemma}
\begin{proof}
proof
\end{proof}

But not sure what to use here, I'm open to some input stylistically of what will look the best, I used enumerate within the lemma environment when I wrote the statement. When I do the proof's right now my code looks something like this:

proof of lemma (4.2) part (1)
\begin{proof}
proof
\end{proof}
proof of lemma (4.2) part (2)
...

However it looks quite unprofessional. Any advice here? Also is it common to restate the lemma I want to prove when I give the proof?