> Here are a few videos which show the automation I used to prove some 
parts of 3cubes (all videos are speechless)

That's impressive!

In all fairness, it's pretty hard to understand what's going on in the 
videos, but it looks like your tactics use a lot of intermediate variables 
in the process (which get eliminated in the end, I guess). I think any 
intermediate variables can be avoided whatsoever. Also I was expecting a 
lot less manual interaction for comparing two polynomials, but I probably 
don't understand some details.

You might know about this already, but mmj2 also has some macros, see 
https://github.com/digama0/mmj2/blob/master/mmj2jar/macros/transformations.js 
Maybe this can serve as inspiration for future work.

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