}\]
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 $D \le C$.
+}
+
\[ \eqn{Totally Foreign Contents:}{
\bigforall_{C \hasparents \set A}
\left[
Contents of $A$, $\patchof{D} = \bot$.
}
-\subsection{No Replay for Merge Results}
-
-If we are constructing $C$, with,
-\gathbegin
- \mergeof{C}{L}{M}{R}
-\gathnext
- L \le C
-\gathnext
- R \le C
-\end{gather}
-No Replay is preserved. \proofstarts
-
-\subsubsection{For $D=C$:} $D \isin C, D \le C$. OK.
-
-\subsubsection{For $D \isin L \land D \isin R$:}
-$D \isin C$. And $D \isin L \implies D \le L \implies D \le C$. OK.
-
-\subsubsection{For $D \neq C \land D \not\isin L \land D \not\isin R$:}
-$D \not\isin C$. OK.
-
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \not\isin M$:}
-$D \isin C$. Also $D \isin L \lor D \isin R$ so $D \le L \lor D \le
-R$ so $D \le C$. OK.
-
-\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
- \land D \isin M$:}
-$D \not\isin C$. OK.
-
-$\qed$
-
\section{Commit annotation}
We annotate each Topbloke commit $C$ with:
Topbloke strips the metadata when exporting.
\subsection{No Replay}
-Trivial.
+
+Ingredients Prevent Replay applies. $\qed$
\subsection{Unique Base}
If $A, C \in \py$ then by Calculation of Ends for
\gathbegin
B \hasparents \{ L \}
\gathnext
- \patchof{B} = \pan{B}
+ \patchof{B} = \pan{Q}
\gathnext
D \isin B \equiv D \isin L \lor D = B
\end{gather}
\patchof{L} = \pa{L} \lor \patchof{L} = \bot
}\]
\[ \eqn{ Non-recursion }{
- L \not\in \pa{B}
+ L \not\in \pa{Q}
}\]
\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}
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.
+xxx this is wrong
+
$\qed$
\subsection{Coherence and Patch Inclusion}
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}
xxx tbd
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 $R^- \le C$.
\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}
\subsection{Foreign Contents}
-Not applicable. $\qed$
+Not applicable.
\section{Merge}
\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}