X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=article.tex;h=8a6bcf4379d7f8748daefd4a1c0f25640c616332;hb=0f66494b88780cc285f36cd0b0e3381e7bfed7a9;hp=84b95b2958b0b59273d62f62ea4a63c7cb655d92;hpb=4adeed6d2972032c54c95f52d4eb74a110685aad;p=topbloke-formulae.git

diff --git a/article.tex b/article.tex
index 84b95b2..8a6bcf4 100644
--- a/article.tex
+++ b/article.tex
@@ -293,6 +293,26 @@ by the LHS.  And $A \le A''$.
 }\]
 xxx proof tbd
 
+\[ \eqn{Ingredients Prevent Replay:}{
+  \left[
+    {C \hasparents \set A} \land
+   \\
+    \left(
+      D \isin C \implies
+       D = C \lor
+       \Largeexists_{A \in \set A} D \isin A
+    \right)
+  \right] \implies \left[
+    D \isin C \implies D \le C
+  \right]
+}\]
+\proof{
+  Trivial for $D = C$.  Consider some $D \neq C$, $D \isin C$.
+  By the preconditions, there is some $A$ s.t. $D \in \set A$
+  and $D \isin A$.  By No Replay for $A$, $D \le A$.  And
+  $A \le C$ so $D \le C$.
+}
+
 \[ \eqn{Totally Foreign Contents:}{
   \bigforall_{C \hasparents \set A}
    \left[
@@ -312,37 +332,6 @@ If $D \neq C$ then $D \le A$ where $A \in \set A$.  By Foreign
 Contents of $A$, $\patchof{D} = \bot$.
 }
 
-\subsection{No Replay for Merge Results}
-
-If we are constructing $C$, with,
-\gathbegin
-  \mergeof{C}{L}{M}{R}
-\gathnext
-  L \le C
-\gathnext
-  R \le C
-\end{gather}
-No Replay is preserved.  \proofstarts
-
-\subsubsection{For $D=C$:} $D \isin C, D \le C$.  OK.
-
-\subsubsection{For $D \isin L \land D \isin R$:}
-$D \isin C$.  And $D \isin L \implies D \le L \implies D \le C$.  OK.
-
-\subsubsection{For $D \neq C \land D \not\isin L \land D \not\isin R$:}
-$D \not\isin C$.  OK.
-
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \not\isin M$:}
-$D \isin C$.  Also $D \isin L \lor D \isin R$ so $D \le L \lor D \le
-R$ so $D \le C$.  OK.
-
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \isin M$:}
-$D \not\isin C$.  OK.
-
-$\qed$
-
 \section{Commit annotation}
 
 We annotate each Topbloke commit $C$ with:
@@ -389,7 +378,8 @@ This also covers Topbloke-generated commits on plain git branches:
 Topbloke strips the metadata when exporting.
 
 \subsection{No Replay}
-Trivial.
+
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 If $A, C \in \py$ then by Calculation of Ends for
@@ -490,19 +480,15 @@ Given $L$, create a Topbloke base branch initial commit $B$.
 
 \subsection{No Replay}
 
-If $\patchof{L} = \pa{L}$, trivial by Base Acyclic for $L$.
-
-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 $D \le B$.
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 
-Not applicable. $\qed$
+Not applicable.
 
 \subsection{Tip Contents}
 
-Not applicable. $\qed$
+Not applicable.
 
 \subsection{Base Acyclic}
 
@@ -523,7 +509,17 @@ and $L \nothaspatch \p \implies B \nothaspatch P$.
 
 $\qed$.
 
-xxx unfinished
+\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.
 
 \section{Create Tip}
 
@@ -557,7 +553,7 @@ 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 $R^- \le C$.
@@ -568,7 +564,10 @@ is a descendant, not an ancestor, of the 2nd parent.)
 
 \subsection{No Replay}
 
-No Replay for Merge Results applies.  $\qed$
+By definition of $\merge$,
+$D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$.
+So, by Ordering of Ingredients,
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Desired Contents}
 
@@ -654,7 +653,7 @@ $\qed$
 
 \subsection{Foreign Contents}
 
-Not applicable. $\qed$
+Not applicable.
 
 \section{Merge}
 
@@ -722,7 +721,10 @@ is therefore consistent with our scheme.
 
 \subsection{No Replay}
 
-No Replay for Merge Results applies.  $\qed$
+By definition of $\merge$,
+$D \isin C \implies D \isin L \lor D \isin R \lor D = C$.
+So, by Ingredients,
+Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}