chiark / gitweb /
 author Ian Jackson Wed, 21 Mar 2012 21:42:22 +0000 (21:42 +0000) committer Ian Jackson Wed, 21 Mar 2012 21:42:22 +0000 (21:42 +0000)
 anticommit.tex patch | blob | history

index e4f5d48..90f2ea4 100644 (file)
@@ -96,23 +96,32 @@ $\implies D \not\in \ply$.  $\qed$.

\subsection{Coherence and Patch Inclusion}

-Need to consider some $D \in \py$.  By Into Base, $D \neq C$.
+$$+\begin{cases} + \p = \pr : & C \nothaspatch \p \\ + \p \neq \pr \land L \nothaspatch \p : & C \nothaspatch \p \\ + \p \neq \pr \land L \haspatch \p : & C \haspatch \p +\end{cases} +$$
+\proofstarts
+~ 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 $C \nothaspatch \pr$.
+OK.

\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 $L \nothaspatch \p \implies C \nothaspatch \p$.
+OK.

Whereas, if $L \haspatch \p$, $D \isin L \equiv D \le L$,
so $C \zhaspatch \p$;
-and $\exists_{F \in \py} F \le L$ so this $F \le C$.
-Thus $\p \neq R \land L \haspatch \p \implies C \haspatch \p$.
+and $\exists_{F \in \py} F \le L$ and this $F \le C$.
+Thus $C \haspatch \p$.
+OK.

$\qed$