simple commit foreign inclusion use simple foreign inclusion

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 69f530a6c3395cf8b6e0e9462612b817ceb9360f..b4035ddf35da3ad1c234a2b42f684784d3fd3485 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -317,6 +317,24 @@ xxx proof tbd
   $A \le C$ so $D \le C$.
 }
 
+\[ \eqn{Simple Foreign Inclusion:}{
+  \left[
+    C \hasparents \{ L \}
+   \land
+    \bigforall_{D} D \isin C \equiv D \isin L \lor D = C
+  \right]
+ \implies
+   \bigforall_{D \text{ s.t. } \patchof{D} = \bot}
+     D \isin C \equiv D \le C
+}\]
+\proof{
+Consider some $D$ s.t. $\patchof{D} = \bot$.
+If $D = C$, trivially true.  For $D \neq C$,
+by Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
+And by Exact Ancestors $D \le L \equiv D \le C$.
+So $D \isin C \equiv D \le C$.
+}
+
 \[ \eqn{Totally Foreign Contents:}{
   \bigforall_{C \hasparents \set A}
    \left[
@@ -452,10 +470,9 @@ So:
 \[ A \nothaspatch P \implies C \nothaspatch P \]
 $\qed$
 
-\subsection{Foreign inclusion:}
+\subsection{Foreign Inclusion:}
 
-If $D = C$, trivial.  For $D \neq C$:
-$D \isin C \equiv D \isin A \equiv D \le A \equiv D \le C$.  $\qed$
+Simple Foreign Inclusion applies.  $\qed$
 
 \subsection{Foreign Contents:}
 
@@ -503,7 +520,8 @@ $D \not\in \pqy$.  $\qed$
 \subsection{Coherence and Patch Inclusion}
 
 Consider some $D \in \p$.
-$B \not\in \py$ so $D \neq B$.  So $D \isin B \equiv D \isin L$.
+$B \not\in \py$ so $D \neq B$.  So $D \isin B \equiv D \isin L$
+and $D \le B \equiv D \le L$.
 
 Thus $L \haspatch \p \implies B \haspatch P$
 and $L \nothaspatch \p \implies B \nothaspatch P$.
@@ -512,11 +530,7 @@ $\qed$.
 
 \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 $D \isin B \equiv D \le B$.  $\qed$
+Simple Foreign Inclusion applies. $\qed$
 
 \subsection{Foreign Contents}
 
@@ -538,6 +552,9 @@ Given a Topbloke base $B$, create a tip branch initial commit B.
 \[ \eqn{ Ingredients }{
  \patchof{B} = \pqn
 }\]
+\[ \eqn{ No Sneak }{
+ \pendsof{B}{\pqy} = \{ \}
+}\]
 
 \subsection{No Replay}
 
@@ -545,7 +562,7 @@ Ingredients Prevent Replay applies.  $\qed$
 
 \subsection{Unique Base}
 
-Trivially, $\pendsof{C}{\pqn} = \{B\}$ so $\baseof{C} = B$.
+Trivially, $\pendsof{C}{\pqn} = \{B\}$ so $\baseof{C} = B$.  $\qed$
 
 \subsection{Tip Contents}
 
@@ -557,6 +574,34 @@ So $D \isin C \equiv D \isin \baseof{B}$.
 
 $\qed$
 
+\subsection{Base Acyclic}
+
+Not applicable.
+
+\subsection{Coherence and Patch Inclusion}
+
+$$
+\begin{cases}
+  \p = \pq    \lor B \haspatch \p : & C \haspatch \p \\
+  \p \neq \pq \land B \nothaspatch \p : & C \nothaspatch \p
+\end{cases}
+$$
+
+\proofstarts
+~ Consider some $D \in \py$.
+
+\subsubsection{For $\p = \pq$:}
+
+By Base Acyclic, $D \not\isin B$.  So $D \isin C \equiv D = C$.
+By No Sneak, $D \le B \equiv D = C$.  Thus $C \haspatch \pq$.
+
+\subsubsection{For $\p \neq \pq$:}
+
+$D \neq C$.  So $D \isin C \equiv D \isin B$,
+and $D \le C \equiv D \le B$.
+
+$\qed$
+
 xxx up to here
 
 \section{Anticommit}