Let $F \subseteq X^{(k)}$ (a layer of the Power set of $X$) be a $k$-uniform family of subsets of $X$ (that is they all have the same size). The (lower) shadow $\partial F$ of $F$ is

$\partial F : = \{B \in X^{(k-1)} : B \subseteq A \text{ for some } A \in F \}$