Solution
= Solution
A <subset> $E\subseteq P$ is <dense above a forcing condition> $p$ if
$$
\boxed{\forall q\ge p\ \exists r\ge q\ (r\in E).}
$$
All displayed strengthenings use the PDF convention. This only requires density in the cone of extensions of $p$; it need not be dense throughout $P$, nor downward or upward closed.