\section{Create Base}

Given a starting point $L$ and a proposed patch $\pq$,
create a Topbloke base branch initial commit $B$.
\gathbegin
 B \hasparents \{ L \}
\gathnext
 \patchof{B} = \pqn
\gathnext
 D \isin B \equiv D \isin L \lor D = B
\end{gather}

\subsection{Conditions}

\[ \eqn{ Create Acyclic }{
 L \nothaspatch \pq
}\]
\[ \eqn{ Ingredients }{
 \patchof L = \foreign \lor \patchof L = \py
}\]

\subsection{No Replay}

Ingredients Prevent Replay applies.  $\qed$

\subsection{Unique Base}

Not applicable.

\subsection{Tip Contents}

Not applicable.

\subsection{Base Acyclic}

Consider some $D \isin B$.  If $D = B$, $D \in \pqn$.
If $D \neq B$, $D \isin L$, so by Create Acyclic
$D \not\in \pqy$.  $\qed$

\subsection{Coherence and Patch Inclusion}

Consider some $D \in \py$.
$B \not\in \py$ so $D \neq B$.  So $D \isin B \equiv D \isin L$
and $D \le B \equiv D \le L$.

Thus $L \haspatch \p \equiv B \haspatch P$
and $L \nothaspatch \p \equiv B \nothaspatch P$.

$\qed$

\subsection{Unique Tips:}

Single Parent Unique Tips applies.  $\qed$

\subsection{Foreign Inclusion}

Simple Foreign Inclusion applies. $\qed$

\subsection{Foreign Ancestry}

Not applicable.

\subsection{Bases' Children}

Not applicable, by Ingredients.
$\qed$
