add purported proof of calculation of ends

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index b48a31ec886c201d1ecd4653d26b6bdbfddd3866..b26a120098b953606abe0fdee77d83abe9543735 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -310,7 +310,16 @@ by the LHS.  And $A \le A''$.
        \right\}
       \end{cases}
 }\]
-xxx proof tbd
+\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 $\pendsof{C}{\set P} \subset \bigcup_{E in \set E} \pendsof{E}{\set P}$.
+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,
+an $F''$) which disqualifies $F$.
+Otherwise, $E$ meets all the conditions for $\pends$.
+}
 
 \[ \eqn{Ingredients Prevent Replay:}{
   \left[