Consider some $E \in \pendsof{A}{\set P}$. If $\exists_{B,F}$ as
specified, then either $F$ is going to be in our result and
disqualifies $E$, or there is some other $F'$ (or, eventually,
-an $F''$) which disqualifies $F$.
+an $F''$) which disqualifies $F$ and $E$.
Otherwise, $E$ meets all the conditions for $\pends$.
}