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strategy: ranking: proof of termination
[topbloke-formulae.git]
/
anticommit.tex
diff --git
a/anticommit.tex
b/anticommit.tex
index cf93fd2998cc593323055552dc92db7c4c11d8e4..2306a73e151075757b87891b3f9d17a447b9d88d 100644
(file)
--- a/
anticommit.tex
+++ b/
anticommit.tex
@@
-19,7
+19,7
@@
R^+ \in \pry \land R^- = \baseof{R^+}
\[ \eqn{ Into Base }{
L \in \pln
}\]
\[ \eqn{ Into Base }{
L \in \pln
}\]
-\[ \eqn{
Unique
Tip }{
+\[ \eqn{
Correct
Tip }{
\pendsof{L}{\pry} = \{ R^+ \}
}\]
\[ \eqn{ Currently Included }{
\pendsof{L}{\pry} = \{ R^+ \}
}\]
\[ \eqn{ Currently Included }{
@@
-28,7
+28,7
@@
R^+ \in \pry \land R^- = \baseof{R^+}
\subsection{Ordering of Ingredients:}
\subsection{Ordering of Ingredients:}
-By
Unique
Tip, $R^+ \le L$. By definition of $\base$, $R^- \le R^+$
+By
Correct
Tip, $R^+ \le L$. By definition of $\base$, $R^- \le R^+$
so $R^- \le L$. So $R^+ \le C$ and $R^- \le C$.
$\qed$
so $R^- \le L$. So $R^+ \le C$ and $R^- \le C$.
$\qed$
@@
-62,7
+62,7
@@
$D \not\isin R^-$. Thus $D \not\isin C$. OK.
By Currently Included, $D \isin L$.
By Tip Own Contents for $R^+$, $D \isin R^+ \equiv D \le R^+$, but
By Currently Included, $D \isin L$.
By Tip Own Contents for $R^+$, $D \isin R^+ \equiv D \le R^+$, but
-by
Unique
Tip, $D \le R^+ \equiv D \le L$.
+by
Correct
Tip, $D \le R^+ \equiv D \le L$.
So $D \isin R^+$.
By Base Acyclic for $R^-$, $D \not\isin R^-$.
So $D \isin R^+$.
By Base Acyclic for $R^-$, $D \not\isin R^-$.
@@
-125,6
+125,10
@@
OK.
$\qed$
$\qed$
+\subsection{Unique Tips:}
+
+Single Parent Unique Tips applies. $\qed$
+
\subsection{Foreign Inclusion}
Consider some $D$ s.t. $\patchof{D} = \bot$. $D \neq C$.
\subsection{Foreign Inclusion}
Consider some $D$ s.t. $\patchof{D} = \bot$. $D \neq C$.