remove a spurious \newpage

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 0615616f7d429a2817d9075b51c78298ce9bc411..763cd820403b748450ebd50a30ef49f816ccf538 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -157,7 +157,7 @@ See Unique Base, below.
 
 \item[ $ C \haspatch \p $ ]
 $\displaystyle \bigforall_{D \in \py} D \isin C \equiv D \le C $.
-~ Informally, $C$ has the contents of $\p$.
+~ Informally, $C$ has all the reachable contents of $\p$.
 
 \item[ $ C \nothaspatch \p $ ]
 $\displaystyle \bigforall_{D \in \py} D \not\isin C $.
@@ -183,7 +183,7 @@ $\displaystyle D \isin C \equiv
 $
 
 \end{basedescript}
-\newpage
+
 \section{Invariants}
 
 We maintain these each time we construct a new commit. \\
@@ -657,11 +657,10 @@ Simple Foreign Inclusion applies.  $\qed$
 
 Not applicable.
 
-\section{Dependency Removal}
+\section{Anticommit}
 
 Given $L$ which contains $\pr$ as represented by $R^+, R^-$.
-Construct $C$ which has $\pr$ removed by applying a single
-commit which is the anticommit of $\pr$.
+Construct $C$ which has $\pr$ removed.
 Used for removing a branch dependency.
 \gathbegin
  C \hasparents \{ L \}
@@ -789,67 +788,6 @@ $\qed$
 
 Not applicable.
 
-\section{Dependency Insertion}
-
-Given $L$ construct $C$ which additionally
-contains $\pr$ as represented by $R^+$ and $R^-$.
-This may even be used for reintroducing a previous-removed branch
-dependency.
-\gathbegin
- C \hasparents \{ L, R^+ \}
-\gathnext
- \patchof{C} = \patchof{L}
-\gathnext
- \mergeof{C}{L}{R^-}{R^+}
-\end{gather}
-
-\subsection{Conditions}
-
-\[ \eqn{ Ingredients }{
- R^- = \baseof{R^+}
-}\]
-\[ \eqn{ Into Base }{
- L \in \pqn
-}\]
-\[ \eqn{ Currently Excluded }{
- L \nothaspatch \pry
-}\]
-\[ \eqn{ Insertion Acyclic }{
- R^+ \nothaspatch \pq
-}\]
-
-\subsection{No Replay}
-
-By $\merge$,
-$D \isin C \implies D \isin L \lor D \isin R^+ \lor D = C$.
-So Ingredients Prevent Replay applies. $\qed$
-
-\subsection{Unique Base}
-
-Not applicable.
-
-\subsection{Tip Contents}
-
-Not applicable.
-
-\subsection{Base Acyclic}
-
-Consider some $D \isin C$.  We will show that $D \not\in \pqy$.
-By $\merge$, $D \isin L \lor D \isin R^+ \lor D = C$.
-
-For $D \isin L$, Base Acyclic for L suffices.  For $D \isin R^+$,
-Insertion Acyclic suffices.  For $D = C$, trivial.  $\qed$.
-
-\subsection{Coherence}
-
-We consider some $D \in \py$.
-
-\subsubsection{For $\p = \pq$:}
-
-xxx up to here
-
-$D \not\isin L$, $D \not\isin $
-
 \section{Merge}
 
 Merge commits $L$ and $R$ using merge base $M$:
@@ -862,6 +800,9 @@ Merge commits $L$ and $R$ using merge base $M$:
 \end{gather}
 We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 
+This can also be used for dependency re-insertion, by setting
+$L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
+
 \subsection{Conditions}
 \[ \eqn{ Ingredients }{
  M \le L, M \le R
@@ -882,15 +823,15 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 }\]
 \[ \eqn{ Removal Merge Ends }{
     X \not\haspatch \p \land
-    Y \haspatch \p \land
-    M \haspatch \p
+    M \haspatch \p \land
+    Y \haspatch \p
   \implies
     \pendsof{Y}{\py} = \pendsof{M}{\py}
 }\]
 \[ \eqn{ Addition Merge Ends }{
     X \not\haspatch \p \land
-    Y \haspatch \p \land
-    M \nothaspatch \p
+    M \nothaspatch \p \land
+    Y \haspatch \p
    \implies \left[
     \bigforall_{E \in \pendsof{X}{\py}} E \le Y
    \right]