leanprover-community / leanprover-community/mathlib4
Sperner's lemma
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Description
Sperner's lemma is a combinatorial statement about some colorings of the triangulations of a triangle. It can be used to prove the Brouwer fixed point theorem.
Bhavik and I had a go at implementing Sperner's lemma in Lean 3 back in 2021 (in fact, Bhavik had an even earlier go). We reduced the problem to some combinatorial statement with geometric input, and found a proof of it, but the effort petered out before that proof was formalised.
I would be happy to supervise someone to take over where we left things off.
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
Start by locating the earlier Lean 3 implementation attempts and the reduced combinatorial statement described in the issue. Trace the unfinished proof and its geometric input; done means formalizing the remaining proof of Sperner's lemma in Lean 4 and adding the resulting theorem to mathlib.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Quiet
- Clarity
- Needs clarification
- Newbie friendliness
- 35/100