}\]
\[ \eqn{ Foreign Unaffected }{
- \bigforall_{ D \text{ s.t. } \patchof{D} = \bot }
- \left[ \bigexists_{A \in \set A} D \le A \right]
- \implies
- D \le L
+ \pendsof{C}{\foreign} = \pendsof{L}{\foreign}
}\]
- TODO THAT IS IMPOSSIBLE TO CALCULATE
\subsection{Lemma: Foreign Identical}
-$\patchof{D} = \bot \implies \big[ D \le C \equiv D \le L \big]$.
+$\isforeign{D} \implies \big[ D \le C \equiv D \le L \big]$.
\proof{
-If $D \le L$, trivially $D \le C$; so conversely
-$D \not\le C \implies D \not\le L$.
-Whereas if $D \le C$, either $D \le L$ or
-$\exists{A \in \set A} D \le A$ (since $D \neq C$),
-in which case by Foreign Unaffected $D \le L$.
+Trivial by Foreign Unaffected and the definition of $\pends$
}
\subsection{No Replay}