And by $Y \haspatch \p$, $\exists_{F \in \py} F \le Y$ and this
$F \le C$ so this suffices.
Consider $D = C$: Thus $C \in \py, L \in \py$.
And by $Y \haspatch \p$, $\exists_{F \in \py} F \le Y$ and this
$F \le C$ so this suffices.
Consider $D = C$: Thus $C \in \py, L \in \py$.