rename merge Ordering of L... to Ordering of Ingredients

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index d3f553ae456bc24b381ff4c3a254996c2073f9c4..73453122e8a9dd7bf549c2df7a6f26edb44a85c5 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -492,23 +492,48 @@ 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}
 
-Not applicable. $\qed$
+Not applicable.
 
 \subsection{Tip Contents}
 
-Not applicable. $\qed$
+Not applicable.
 
 \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 $L \nothaspatch \p \implies B \nothaspatch P$.
+
+$\qed$.
+
+\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}
 
-xxx unfinished
+Not applicable.
 
 \section{Create Tip}
 
@@ -542,7 +567,7 @@ R^+ \in \pry \land R^- = \baseof{R^+}
  L \haspatch \pry
 }\]
 
-\subsection{Ordering of ${L, R^+, R^-}$:}
+\subsection{Ordering of Ingredients:}
 
 By Unique Tip, $R^+ \le L$.  By definition of $\base$, $R^- \le R^+$
 so $R^- \le L$.  So $R^+ \le C$ and $R^- \le C$.
@@ -639,7 +664,7 @@ $\qed$
 
 \subsection{Foreign Contents}
 
-Not applicable. $\qed$
+Not applicable.
 
 \section{Merge}