fix up some lemmas re ends

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 9a0cf07790e56d6f778ce8ff8ee244b546533fd7..b4f7beb8b8ea8ea6a82a3422bfaedd37cfeb853b 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -254,6 +254,7 @@ $ \bigforall_{C \in \py}\bigforall_{D \in \py}
     ( \mathop{\hbox{\huge{$\vee$}}}_{R \in \set R} D \le R )
     \lor D = C
 }\]
+xxx proof tbd
 
 \[ \eqn{Transitive Ancestors:}{
   \left[ \bigforall_{ E \in \pendsof{C}{\set P} } E \le M \right] \equiv
@@ -272,17 +273,23 @@ in which case we repeat for $A'$.  Since there are finitely many
 commits, this terminates with $A'' \in \pends()$, ie $A'' \le M$
 by the LHS.  And $A \le A''$.
 }
+
 \[ \eqn{Calculation Of Ends:}{
   \bigforall_{C \hasparents \set A}
     \pendsof{C}{\set P} =
+      \begin{cases}
+       C \in \p : & \{ C \}
+      \\
+       C \not\in \p : & \displaystyle
        \left\{ E \Big|
            \Bigl[ \Largeexists_{A \in \set A} 
                        E \in \pendsof{A}{\set P} \Bigr] \land
            \Bigl[ \Largenexists_{B \in \set A} 
                        E \neq B \land E \le B \Bigr]
        \right\}
+      \end{cases}
 }\]
-XXX proof TBD.
+xxx proof tbd
 
 \subsection{No Replay for Merge Results}