chiark / gitweb /
 author Ian Jackson Mon, 26 Mar 2012 00:17:32 +0000 (01:17 +0100) committer Ian Jackson Mon, 26 Mar 2012 00:17:32 +0000 (01:17 +0100)
 lemmas.tex patch | blob | history

index efffe6b..41ea1c8 100644 (file)
@@ -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,