X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=article.tex;h=7630745d41eaf60ca7369bd99e7ec29ea03cbe98;hp=a86c22050a44b1316d629e4a33a56b1df63978b8;hb=c2932ba812fa6fdf7b03615dd4a8709449cd8983;hpb=89a887de02bb460be749f19b63735f23d9db5ea0

diff --git a/article.tex b/article.tex
index a86c220..7630745 100644
--- a/article.tex
+++ b/article.tex
@@ -196,6 +196,10 @@ We maintain these each time we construct a new commit. \\
 \[\eqn{Foreign Inclusion:}{
   \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
 }\]
+\[\eqn{Foreign Contents:}{
+  \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
+    D \le C \implies \patchof{D} = \bot
+}\]
 
 \section{Some lemmas}
 
@@ -289,6 +293,21 @@ by the LHS.  And $A \le A''$.
 }\]
 xxx proof tbd
 
+\[ \eqn{Totally Foreign Contents:}{
+  \bigforall_{C \hasparents \set A}
+   \left[
+    \patchof{C} = \bot \land
+      \bigforall_{A \in \set A} \patchof{A} = \bot
+   \right]
+  \implies
+   \left[
+    D \isin C
+   \implies
+    \patchof{D} = \bot
+   \right]
+}\]
+xxx proof tbd
+
 \subsection{No Replay for Merge Results}
 
 If we are constructing $C$, with,
@@ -442,11 +461,49 @@ $D \isin C \equiv D \isin A \equiv D \le A \equiv D \le C$.  $\qed$
 
 \section{Create Base}
 
-xxx tbd
+Given $L$, create a Topbloke base branch initial commit $B$.
+\gathbegin
+ B \hasparents \{ L \}
+\gathnext
+ \patchof{B} = \pa{B}
+\gathnext
+ D \isin B \equiv D \isin L \lor D = B
+\end{gather}
+
+\subsection{Conditions}
+
+\[ \eqn{ Ingredients }{
+ \patchof{L} = \pa{L} \lor \patchof{L} = \bot
+}\]
+\[ \eqn{ Non-recursion }{
+ L \not\in \pa{B}
+}\]
+
+\subsection{No Replay}
+
+If $\patchof{L} = \pa{L}$, trivial by Base Acyclic for $L$.
+
+If $\patchof{L} = \bot$, xxx
+
+Trivial from Base Acyclic for $L$.  $\qed$
+
+\subsection{Unique Base}
+
+Not applicable. $\qed$
+
+\subsection{Tip Contents}
+
+Not applicable. $\qed$
+
+\subsection{Base Acyclic}
+
+xxx
+
+xxx unfinished
 
 \section{Create Tip}
 
-xxx tbd\
+xxx tbd
 
 \section{Anticommit}
 
@@ -560,7 +617,7 @@ so $L \haspatch \p \implies C \haspatch \p$.
 
 $\qed$
 
-\section{Foreign Inclusion}
+\subsection{Foreign Inclusion}
 
 Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq C$.
 So by Desired Contents $D \isin C \equiv D \isin L$.