create base coherence fix title

diff --git a/article.tex b/article.tex
index d3f553ae456bc24b381ff4c3a254996c2073f9c4..84b95b2958b0b59273d62f62ea4a63c7cb655d92 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -492,9 +492,9 @@ Given $L$, create a Topbloke base branch initial commit $B$.
 
 If $\patchof{L} = \pa{L}$, trivial by Base Acyclic for $L$.
 
-If $\patchof{L} = \bot$, xxx
-
-Trivial from Base Acyclic for $L$.  $\qed$
+If $\patchof{L} = \bot$, consider some $D \isin B$.  $D \neq B$.
+Thus $D \isin L$.  So by No Replay of $D$ in $L$, $D \le L$.
+Thus $D \le B$.
 
 \subsection{Unique Base}
 
@@ -506,7 +506,22 @@ Not applicable. $\qed$
 
 \subsection{Base Acyclic}
 
-xxx
+Consider some $D \isin B$.  If $D = B$, $D \in \pn$, OK.
+
+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 $L \nothaspatch \p \implies B \nothaspatch P$.
+
+$\qed$.
 
 xxx unfinished