Getting cozy with weekly PITR

Hello,

Thanks for advice/suggestions on PITR so far.

We have finally decided to do weekly PITR base backups. Just have one
nagging question.

== week 1==-
* pg_start_backup()
* tar -cvzf basebackup_week1.tar.gz pgdata/
* pg_stop_backup()

cp WAL1 week1/wal/
..
cp WAL2 week1/wal/
==*==

Week 1, we perform base backup and WAL will be backed up by PG.

==week 2==
* pg_start_backup()
* tar -cvzf basebackup_week2.tar.gz pgdata
* pg_stop_backup()
cp WAL1 week2/wal/
...
cp WAL2 week2/wal
...
rm -f basebackup_week1.tar.gz
rm -rf week1/wal
==*==

During week 2, after the base backup, can we remove week 1's base and WAL
files?

I assume this is okay since week 2's PITR backup is as good as new but just
wanted to be doubly sure about it before we get rid of week 1's backup.

Steve