Is \$$\leq\$$ properly defined in **Puzzle 193**? I think we should have \$$I\leq S\$$ for all \$$S\in P(X)\$$, but it is not true that \$$X\subseteq S\$$ (unless \$$X=S\$$). If, instead, we use the reverse inclusion, I think \$$P(X)\$$ is not a closed monoidal poset.