a todo item

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 0688c7ad02524d0d5c0d399682f3ac46946d1e1f..9a60dcd5e4ef440502cace7e6ac687a704dec37d 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -95,6 +95,8 @@
 
 \section{Notation}
 
+xxx make all conditions be in conditions, not in (or also in) intro
+
 \begin{basedescript}{
 \desclabelwidth{5em}
 \desclabelstyle{\nextlinelabel}
@@ -429,7 +431,7 @@ Used for removing a branch dependency.
 
 \subsection{Conditions}
 
-\[ \eqn{ From Base }{
+\[ \eqn{ Into Base }{
  L \in \pn
 }\]
 \[ \eqn{ Unique Tip }{
@@ -439,11 +441,17 @@ Used for removing a branch dependency.
  L \haspatch \pry
 }\]
 
-\subsection{No Replay}
+\subsection{Ordering of ${L, R^+, R^-}$:}
 
 By Unique Tip, $R^+ \le L$.  By definition of $\base$, $R^- \le R^+$
-so $R^- \le L$.  So $R^+ \le C$ and $R^- \le C$ and No Replay for
-Merge Results applies. $\qed$
+so $R^- \le L$.  So $R^+ \le C$ and $R^- \le C$.
+
+(Note that the merge base $R^+ \not\le R^-$, i.e. the merge base is
+later than one of the branches to be merged.)
+
+\subsection{No Replay}
+
+No Replay for Merge Results applies.  $\qed$
 
 \subsection{Desired Contents}
 
@@ -481,16 +489,53 @@ $\qed$
 
 \subsection{Unique Base}
 
-From Base means that $C \in \pn$, so Unique Base is not
+Into Base means that $C \in \pn$, so Unique Base is not
 applicable. $\qed$
 
 \subsection{Tip Contents}
 
 Again, not applicable. $\qed$
 
-xxx tbd
+\subsection{Base Acyclic}
+
+By Base Acyclic for $L$, $D \isin L \implies D \not\in \py$.
+And by Into Base $C \not\in \py$.
+Now from Desired Contents, above, $D \isin C
+\implies D \isin L \lor D = C$, which thus
+$\implies D \not\in \py$.  $\qed$.
+
+\subsection{Coherence and Patch Inclusion}
+
+Need to consider some $D \in \py$.  By Into Base, $D \neq C$.
+
+\subsubsection{For $\p = \pr$:}
+By Desired Contents, above, $D \not\isin C$.
+So $C \nothaspatch \pr$.
+
+\subsubsection{For $\p \neq \pr$:}
+By Desired Contents, $D \isin C \equiv D \isin L$
+(since $D \in \py$ so $D \not\in \pry$).
+
+If $L \nothaspatch \p$, $D \not\isin L$ so $D \not\isin C$.
+So $L \nothaspatch \p \implies C \nothaspatch \p$.
+
+Whereas if $L \haspatch \p$, $D \isin L \equiv D \le L$.
+so $L \haspatch \p \implies C \haspatch \p$.
+
+\section{Foreign Inclusion}
+
+Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq C$.
+So by Desired Contents $D \isin C \equiv D \isin L$.
+By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
+So $D \isin C \equiv D \le L$.
+
+xxx up to here
+
+By Tip Contents of $R^+$, $D \isin R^+ \equiv D \isin \baseof{R^+}$
+i.e. $\equiv D \isin R^-$.
+So by $\merge$, $D \isin C \equiv D \isin L$.
 
-xxx need to finish anticommit
+Thus $D \isin C \equiv $
 
 \section{Merge}
 
@@ -549,7 +594,7 @@ Merge Ends condition applies.  Good.
 
 \subsection{No Replay}
 
-See No Replay for Merge Results.
+No Replay for Merge Results applies.  $\qed$
 
 \subsection{Unique Base}
 
@@ -623,7 +668,8 @@ So indeed $L \haspatch \p \land R \haspatch \p \implies C \haspatch \p$.
 
 \subsubsection{For (wlog) $X \not\haspatch \p, Y \haspatch \p$:}
 
-$C \haspatch \p \equiv M \nothaspatch \p$.
+$M \haspatch \p \implies C \nothaspatch \p$.
+$M \nothaspatch \p \implies C \haspatch \p$.
 
 \proofstarts