$D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$.
So, by Ordering of Ingredients,
Ingredients Prevent Replay applies. $\qed$
$D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$.
So, by Ordering of Ingredients,
Ingredients Prevent Replay applies. $\qed$
\subsubsection{For $D \neq C, D \le L, D \notin \pry$:}
By Tip Contents for $R^+$, $D \isin R^+ \equiv D \isin R^-$.
\subsubsection{For $D \neq C, D \le L, D \notin \pry$:}
By Tip Contents for $R^+$, $D \isin R^+ \equiv D \isin R^-$.
So by Desired Contents $D \isin C \equiv D \isin L$.
By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
So by Desired Contents $D \isin C \equiv D \isin L$.
By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.