Hi all,

Some time ago, I wrote a script implementing the completeness theorem for
propositional calculus in the form of a tautology prover for Metamath. I
just uploaded it to Github. You can find it at
https://github.com/sctfn/completeness.

To use the script to prove biid, you would call "./completeness biid '( ph
<-> ph )'". This will produce an uncompressed $p statement that you can
incorporate into set.mm. Furthermore, if called with the "-d" flag, the
script will instead produce a D-rule proof of the theorem.

Let me know what you think!

-Scott

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