Foreign Contents section in a couple of places

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 73217528caf6f8329960297c22fc687353e5fecf..3d8bd8179a5f26dc787fa70a4de9046f32709f6d 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -196,6 +196,10 @@ We maintain these each time we construct a new commit. \\
 \[\eqn{Foreign Inclusion:}{
   \bigforall_{D \text{ s.t. } \patchof{D} = \bot} D \isin C \equiv D \leq C
 }\]
+\[\eqn{Foreign Contents:}{
+  \bigforall_{C \text{ s.t. } \patchof{C} = \bot}
+    D \le C \implies \patchof{D} = \bot
+}\]
 
 \section{Some lemmas}
 
@@ -289,6 +293,21 @@ by the LHS.  And $A \le A''$.
 }\]
 xxx proof tbd
 
+\[ \eqn{Totally Foreign Contents:}{
+  \bigforall_{C \hasparents \set A}
+   \left[
+    \patchof{C} = \bot \land
+      \bigforall_{A \in \set A} \patchof{A} = \bot
+   \right]
+  \implies
+   \left[
+    D \isin C
+   \implies
+    \patchof{D} = \bot
+   \right]
+}\]
+xxx proof tbd
+
 \subsection{No Replay for Merge Results}
 
 If we are constructing $C$, with,
@@ -440,6 +459,13 @@ $\qed$
 If $D = C$, trivial.  For $D \neq C$:
 $D \isin C \equiv D \isin A \equiv D \le A \equiv D \le C$.  $\qed$
 
+\subsection{Foreign Contents:}
+
+Only relevant if $\patchof{C} = \bot$.  Trivial by Foreign Contents of
+$A$.  $\qed$
+
+xxx fixme not trivial use Totally Foreign Contents
+
 \section{Create Base}
 
 Given $L$, create a Topbloke base branch initial commit $B$.
@@ -609,6 +635,10 @@ Thus $D \isin C \equiv D \le C$.
 
 $\qed$
 
+\subsection{Foreign Contents:}
+
+Not applicable. $\qed$
+
 \section{Merge}
 
 Merge commits $L$ and $R$ using merge base $M$:
@@ -869,4 +899,11 @@ OK
 
 $\qed$
 
+\subsection{Foreign Contents:}
+
+xxx use Totally Foreign Contents
+
+If $\patchof{C} = \bot$, by Foreign Merges
+$\patchof{L} = \patchof{R} = \bot$.
+
 \end{document}