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closes issue ualib#190
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JacquesCarette committed Apr 26, 2022
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(addressed point c)

(Other than 'choosing setoids', very little, for part a. Our setup is the same as that of
Abel [1]. Capretta [5] uses setoids as well, but not universes since Coq doesn't "really".
It is hard to compare with [2], since their aim and ours are quite different, but it would be useful
to do so in the future. Our work is strictly more general than that of [11], which also uses
setoids, but restricts itself to finitary arities, which makes things "messy". [14] is quite
different, being in HoTT-UniMath, multi-sorted yet finitary. And yet, a lot of the 'results'
end up involving very similar statements. In other words, universal algebra seems to be quite
foundations-independent, at some level that should be investigated in the future)

4. ~~Some links are broken (e.g. in [8]); some footnotes need to have first letters capitalised.~~ (fixed)


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algebras in S K, as in §6.2, would be forbidden because of size issues (e.g., let K be the class of all
algebras with empty signature).

(A discussion section has been added for this)

4. > ~~To the best of our knowledge, this constitutes~~
> ~~the first machine-verified proof of Birkoff's celebrated 1935 result.~~
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