+If $D \neq B$, $D \isin L$. By No Replay of $D$ in $L$, $D \le L$.
+Thus by Foreign Contents of $L$, $\patchof{D} = \bot$. OK.
+
+$\qed$
+
+\subsection{Coherence and Patch Inclusion}
+
+Consider some $D \in \p$.
+$B \not\in \py$ so $D \neq B$. So $D \isin B \equiv D \isin L$.
+
+Thus $L \haspatch \p \implies B \haspatch P$
+and $L \nothaspatch \p \implies B \nothaspatch P$.
+
+$\qed$.
+
+\subsection{Foreign Inclusion}
+
+Consider some $D$ s.t. $\patchof{D} = \bot$. $D \neq B$
+so $D \isin B \equiv D \isin L$.
+By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
+And by Exact Ancestors $D \le L \equiv D \le B$.
+So $D \isin B \equiv D \le B$. $\qed$
+
+\subsection{Foreign Contents}
+
+Not applicable.