From 4c0c56b9bf2a14d4cd0d90d9826d471da7483c14 Mon Sep 17 00:00:00 2001 From: Ian Jackson Date: Mon, 26 Mar 2012 01:17:32 +0100 Subject: [PATCH] fix notation in calculation of ends --- lemmas.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/lemmas.tex b/lemmas.tex index efffe6b..41ea1c8 100644 --- a/lemmas.tex +++ b/lemmas.tex @@ -103,13 +103,13 @@ $$\bigforall_{C \hasparents \set A} \pendsof{C}{\set P} = \begin{cases} - C \in \p : & \{ C \} + C \in \set P : & \{ C \} \\ - C \not\in \p : & \displaystyle + C \not\in \set P : & \displaystyle \left\{ E \Big| \Bigl[ \Largeexists_{A \in \set A} E \in \pendsof{A}{\set P} \Bigr] \land - \Bigl[ \Largenexists_{B \in \set A, F \in \pendsof{B}{\p}} + \Bigl[ \Largenexists_{B \in \set A, F \in \pendsof{B}{\set P}} E \neq F \land E \le F \Bigr] \right\} \end{cases} @@ -117,7 +117,7 @@$$ \proof{ Trivial for $C \in \set P$. For $C \not\in \set P$, $\pancsof{C}{\set P} = \bigcup_{A \in \set A} \pancsof{A}{\set P}$. -So $\pendsof{C}{\set P} \subset \bigcup_{E in \set E} \pendsof{E}{\set P}$. +So $\pendsof{C}{\set P} \subset \bigcup_{E \in \set E} \pendsof{E}{\set P}$. Consider some $E \in \pendsof{A}{\set P}$. If $\exists_{B,F}$ as specified, then either $F$ is going to be in our result and disqualifies $E$, or there is some other $F'$ (or, eventually, -- 2.1.4