Consider $D = C$: Thus $C \in \py, L \in \py$.
By Tip Own Contents, $\neg[ L \nothaspatch \p ]$ so $L \neq X$,
therefore we must have $L=Y$, $R=X$.
By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so
by Base Acyclic $M \nothaspatch \p$. By $\merge$, $D \isin C$,
Consider $D = C$: Thus $C \in \py, L \in \py$.
By Tip Own Contents, $\neg[ L \nothaspatch \p ]$ so $L \neq X$,
therefore we must have $L=Y$, $R=X$.
By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so
by Base Acyclic $M \nothaspatch \p$. By $\merge$, $D \isin C$,