Litex: Formal math for everyone – set theory examples with Lean comparison

[Litex](https://litexlang.com) is a simple open-source computer language for mathematical proofs. Anyone can have a rough understanding of Litex in 2 hours.

Although it is not yet ready for production use, it is already powerful enough to formalize set theory and basic logic, which is enough for most daily mathematical proofs. Visit [Set Theory Examples](https://litexlang.com/doc/How_Litex_Works/Litex_vs_Lean_Set_...) for more examples.

Star the repo [here](https://github.com/litexlang/golitex) to support Litex, and join our [Zulip community](https://litex.zulipchat.com/join/c4e7foogy6paz2sghjnbujov/) to give us feedback and suggestions!

Almost looks like the highlight and default colors got swapped - ctrl+a to read looks ok, but oof.

Litex is probably closer to TLA+ than to Lean. Both draw inspiration from untyped set theory and LaTeX.

One thing I never understood about this: why does this not just compile to Lean so they're compatible with each other? Having a good interface is admirable, but the difference between set and type based foundations seems not very important and porting any enough math to sustain Litex seems like a huge undertaking.

It's truely great if Litex does compile to existing formal languages. The only problem is that we can not find a good way to compile our verification process, which does not require users to give names to facts they are using and thus very different from how Lean works, to Lean (set theory example is just the first one of a series of comparisons). Besides, it's even harder to compile future functionaliteies, like printing out results of each statement of litex in a human readable way, to lean. So since litex is still a young language and we are using our limited resources to try new ideas and crack here and there, for the time being we believe it's not a good time to migrate our code in such a great scale. Thank you. Merry Christmas.