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I had a bit of time and progressed this in #617. It should be merged once reviewed, but does not resolve this issue by itself.
Why didn't I claim this?
Because I have no time to work on it and won't for many weeks. But there's not much left: if you're reading this, I encourage you to claim it and take it up!
What remains to be done?
The survey of examples should be extended with a guide to a greedy argument. The surveyed examples are picked so that they are simple, but not trivial: the aim is not to showcase the most "powerful" applications of each technique, but to provide an accessible entrypoint for people who wish to study them. I think Pace Nielsen's greedy argument for 1701->3 is particularly good for this, but that should be done once #506 is merged (it's not clear until then whether to explain the final proof or the original).
If by that point this list will have expanded with important new techniques specifically for infinite magmas, a stub can be created for examples as well.
See this discussion for a proposed sketch of the new chapter.
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