\subsubsection{For $\p \neq \pr$:}
By Desired Contents, $D \isin C \equiv D \isin L$
(since $D \in \py$ so $D \not\in \pry$).
If $L \nothaspatch \p$, $D \not\isin L$ so $D \not\isin C$.
\subsubsection{For $\p \neq \pr$:}
By Desired Contents, $D \isin C \equiv D \isin L$
(since $D \in \py$ so $D \not\in \pry$).
If $L \nothaspatch \p$, $D \not\isin L$ so $D \not\isin C$.