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# Lean4 port of the proof of Rubin's Theorem
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THis repository contains a (WIP) computer proof of Rubin's Theorem,
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which states that two groups (which satisfy a few conditions) that act on a topological space have a homeomorphism between them,
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such that the homeomorphism preserves the group structure.
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It is based on ["A short proof of Rubin's Theorem"](https://arxiv.org/abs/2203.05930) (James Belk, Luke Elliott and Franceso Matucci),
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and a good part of the computer proof was written in Lean 3 by [Laurent Bartholdi](https://www.math.uni-sb.de/ag/bartholdi/).
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The eventual goal of this computer proof is to have it land into [Mathlib](https://github.com/leanprover-community/mathlib4).
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## Installation and running
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You will need an installation of [`elan`](https://github.com/leanprover/elan) and `git`.
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Then, simply run the following:
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```sh
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# Clone this repository
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git clone https://github.com/adri326/rubin-lean4
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# Navigate to the folder created by git
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cd rubin-lean4
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# This will download mathlib, and try to download a set of pre-compiled .olean files,
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# so you won't have to re-compile the entirety of mathlib again (which takes a good hour or two)
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lake exe cache get
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# Build the code (if no errors are printed then Lean was happy)
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lake build
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```
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