>As you said, there should still be some pondering before adding a theorem, 
even with a high score. 

I think the main criterion should be whether the suggested theorem makes 
any mathematical sense. For example, no. 6 from the list doesn't make any 
sense to me, and it's definitely not a theorem which would come to my mind 
when formalizing a proof. Thus I would argue against adding it to set.mm 
even if it saves a few kilobytes of the database size, since it would 
hinder readability of set.mm proofs.

On the other hand, test4 (now toponrestid in set.mm) looks like a 
reasonable lemma which was often re-proven over and over. Finding these 
kinds of lemmata is, I think, the ultimate goal.

> A possibility is that a theorem appears in this list because a proof 
pattern occurs often.  It could be that this proof pattern can be shortened 
in other ways, but if the theorem in the list is added, the resulting 
shortened proofs will not allow this kind of proof inspection.  Of course 
it's not specific to the present list: the more lemmas are used in a proof, 
the more difficult a global minimization is.

Perhaps a better solution then would be to run full minimize on affected 
theorems instead of minimize_with, so we can give metamath.exe a chance to 
shorten the proof in other ways before applying a new lemma?

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