# Cluster mempool definitions & theory

**URL:** <https://delvingbitcoin.org/t/cluster-mempool-definitions-theory/202>\
**Category:** Implementation\
**Tags:** wg-cluster-mempool\
**Created:** [November 17, 2023, 2:40am UTC](https://delvingbitcoin.org/t/cluster-mempool-definitions-theory/202 "2023-11-17T02:40:41Z")\
**Posts on this page:** 1\
**Showing post:** 10

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**Author:** ![Crypt-iQ](https://delvingbitcoin.org/user_avatar/delvingbitcoin.org/crypt-iq/32/306_2.png) [@Crypt-iQ](https://delvingbitcoin.org/u/Crypt-iQ)\
**Post date:** [February 26, 2024, 11:36pm UTC](https://delvingbitcoin.org/t/cluster-mempool-definitions-theory/202/10 "2024-02-26T23:36:49Z")

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> [@sipa](#):
>
> By repeatedly applying the gathering and stripping theorem, L\_{opt}' \gtrsim L\_{opt}.

I’m a bit confused here; could you elaborate on how the gathering and stripping theorems are used here? Since the gathering theorem applies when a sublinearization is moved to the front, it alone doesn’t prove that L\_{opt}' \gtrsim L\_{opt} since L[p] is the ordering from L rather than from L\_{opt}. I’m not sure where the prefix stripping theorem comes in, so I must be missing something.

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