\end{cases}
}\]
-\subsection{Tip Self Inpatch}
-Given Exclusive Tip Contents and Base Acyclic for $C$,
+\subsection{Tip Own Contents}
+Given Base Acyclic for $C$,
$$
\bigforall_{C \in \py} C \haspatch \p
$$
\proof{
Apply Exclusive Tip Contents to some $D \in \py$:
$ \bigforall_{C \in \py}\bigforall_{D \in \py}
- D \isin C \equiv D \le C $
+ D \isin C \equiv D \le C $.
+Thus $C \zhaspatch \p$.
+And we can set $F=C$ giving $F \in \py \land F \le C$, so $C \haspatch \p$.
}
\subsection{Exact Ancestors}
}
\subsection{Ingredients Prevent Replay}
+Given conformant commits $A \in \set A$,
$$
\left[
{C \hasparents \set A} \land
$$
\proof{
Trivial for $D = C$. Consider some $D \neq C$, $D \isin C$.
- By the preconditions, there is some $A$ s.t. $D \in \set A$
+ By the preconditions, there is some $A$ s.t. $A \in \set A$
and $D \isin A$. By No Replay for $A$, $D \le A$. And
$A \le C$ so $D \le C$.
}
\subsection{Simple Foreign Inclusion}
+Given a conformant commit $L$,
$$
\left[
C \hasparents \{ L \}
}
\subsection{Totally Foreign Contents}
+Given conformant commits $A \in \set A$,
$$
\left[
C \hasparents \set A \land