Proof of sparsification lemma: What exactly does the $\pi$ operator do?
From the definition you gave, the supersets have to be removed, as you want to keep only those sets for which there is no proper subset in $\mathcal{F}$.

For example:



In blue are the sets of $\mathcal{F}$ which don't have proper subsets in $\mathcal{F}$, in red are the ones who do. You want to keep the blue ones, by definition of $\pi$.