  We say that a set system $\mathcal{F}\subseteq 2^{[n]}$ shatters a given set
$S\subseteq [n]$ if $2^S= \{F~\cap~S:~F~\in~\mathcal{F}\}$. The Sauer-Shelah
lemma states that in general, a set system $\mathcal{F}$ shatters at least
$|\mathcal{F}|$ sets. Here we concentrate on the case of equality. A set system
is called \emph{shattering-extremal} if it shatters exactly $|\mathcal{F}|$
sets. A conjecture of R\'onyai and the second author and of Litman and Moran
states that if a family is shattering-extremal then one can add a set to it and
the resulting family is still shattering-extremal. Here we prove this
conjecture for a class of set systems defined from Sperner families.
