> I'm not sure if it's good to pose puzzles that use concepts beyond what's covered in the lectures. (John?)
One problems is that we have about 250 people registered for the course, and a much smaller number of very active participants. If we keep focusing attention on the most knowledgeable students, the others will become increasingly scared to join the conversation. I _wish_ we had lots of comments asking basic questions about the lectures. Unfortunately we don't - and I don't think it's because everything I write is so clear that nobody could conceivably have a question.
On the other hand, it's mainly my responsibility, not yours, to think about these things.
To reduce the intimidation effect, it added a link to a definition of "semilattice" in your question. If someone carefully examines everything in that link, your question becomes much easier.