> There you go: (solution of Day 20)

Thanks! I haven't been able to find this proof anywhere in the literature, 
so this might be a useful reference for some other people as well. There 
seems to be ongoing work on formalizing modal logics in HOL Light, in 
particular, they have an automatic prover for 
GL https://link.springer.com/article/10.1007/s10817-023-09677-z Maybe in 
the worst case one could try to extract the proof from this utility, though 
I'm not sure if it's possible.

> So far, I made almost all proofs by hand (in metamath.exe) without any 
help. ...

I've been using metamath lamp to formalize the proofs, and I've been 
sometimes wondering if its proof searching utility is missing some short 
arguments. I haven't tried comparing it with metamath.exe's improve 
command, though.

> Note: I believe ~puzzlelem requires ~ax-gl for its proof, even tho there 
was no "now you can use ~ax-gl again" in the comment.

Yes, days 21 - 24 are "ax-gl free", and at day 25 you're allowed to use 
ax-gl again.

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