Hmm. elsb4 has an extra distinct variable condition (x and y must be 
different), which the original theorem does not have. I did not look at the 
other results, but some care is in order, I think.

Wolf

David A. Wheeler schrieb am Freitag, 3. Juli 2020 um 16:02:18 UTC+2:

>
> >We've run another search for shorter proofs. There are quite a few and
> >it's unclear how the group wants to handle them so we decided to
> >simply dump them so that everyone can get a chance to review them and
> >pick what they feel is useful.
>
> I'm remote and can't review the files right now, but I think in principle 
> we should simply follow our current rules:
>
> - We should normally never add axioms to a non-ALT proof. We should try to 
> remove Axiom use, especially the Axiom of choice. During this persistently 
> overtime reduces the number of axioms all theorems depend on, even 
> indirectly.
>
> - If there is a proof that uses more axioms but is significantly shorter, 
> we often add them as ALT theorems. When in doubt, I think we should add 
> them as alt theorems. Not everyone cares about minimizing the number of 
> axioms, and the full use of axioms can produce much clearer and shorter 
> proofs.
>
> - We normally do not keep longer proofs unless they demonstrate something 
> important. But if you see a longer proof that should be kept, make it an 
> ALT proof. We have version control, so we can always restore something 
> later if desired.
>
> - Whoever does significant shortening should be credited, e.g., 
> "(Shortened by OpenAI)".
>
> it may take a little time to process a lot of results, but I see that as a 
> very happy problem.
>
> --- David A.Wheeler
>

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