Solution
= Solution
For a condition $p\in\mathbb P$, a set $D\subseteq\mathbb P$ is <dense below a forcing condition> $p$ when
$$
\boxed{\forall q\leq p\ \exists r\leq q\ (r\in D).}
$$
Thus every extension of $p$ can be strengthened into $D$.
= Solution
For a condition $p\in\mathbb P$, a set $D\subseteq\mathbb P$ is <dense below a forcing condition> $p$ when
$$
\boxed{\forall q\leq p\ \exists r\leq q\ (r\in D).}
$$
Thus every extension of $p$ can be strengthened into $D$.