$\qed$
-\subsection{Coherence and patch inclusion}
+\subsection{Coherence and Patch Inclusion}
Need to determine $C \haspatch \p$ based on $L,M,R \haspatch \p$.
This involves considering $D \in \py$.
We need worry only about $C \in \py$.
And $\patchof{C} = \patchof{L}$
-so $L \in \py$ so $L \haspatch \p$. We will use the unique base,
-and coherence and patch inclusion, of $C$ as just proved.
+so $L \in \py$ so $L \haspatch \p$. We will use the Unique Base
+of $C$, and its Coherence and Patch Inclusion, as just proved.
Firstly we show $C \haspatch \p$: If $R \in \py$, then $R \haspatch
-\p$ and by coherence/inclusion $C \haspatch \p$ . If $R \not\in \py$
+\p$ and by Coherence/Inclusion $C \haspatch \p$ . If $R \not\in \py$
then by Tip Merge $M = \baseof{L}$ so by Base Acyclic and definition
-of $\nothaspatch$, $M \nothaspatch \p$. So by coherence/inclusion $C
+of $\nothaspatch$, $M \nothaspatch \p$. So by Coherence/Inclusion $C
\haspatch \p$ (whether $R \haspatch \p$ or $\nothaspatch$).
-We will consider some $D$ and prove the Exclusive Tip Contents form.
+We will consider an arbitrary commit $D$
+and prove the Exclusive Tip Contents form.
\subsubsection{For $D \in \py$:}
$C \haspatch \p$ so by definition of $\haspatch$, $D \isin C \equiv D