leanprover-community / leanprover-community/mathlib4
refactor: generalize `LocallyFinite.exists_finset_nhd_mulSupport_subset`
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Description
This lemma has (almost) nothing to do with support of a function. In fact, it is a lemma about a locally finite family of sets s and a family of open sets U such that closure (s i) ⊆ U i.
- Generalize, prove the old version in 1 line (can be done at any time). Possibly, deprecate the old version.
- Delete the old lemma.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Locate LocallyFinite.exists_finset_nhd_mulSupport_subset and read its statement and surrounding lemmas first. Generalize it to locally finite families of sets with closure (s i) ⊆ U i, then verify the old support-specific version can be proved in one line and determine whether the old lemma should be deprecated or deleted.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Refactor
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 35/100