wip traversal

[topbloke-formulae.git] / lemmas.tex

diff --git a/lemmas.tex b/lemmas.tex
index 83fc3f69d6048a9446271e5e235bc3dcae792afc..23e22f3285bbc2ec8544714a1ed4d8a04479121d 100644 (file)
--- a/lemmas.tex
+++ b/lemmas.tex
@@ -1,6 +1,6 @@
 \section{Some lemmas}
 
-\subsection{Alternative (overlapping) formulations of $\mergeof{C}{L}{M}{R}$}
+\subsection{Alternative (overlapping) formulations of $\commitmergeof{C}{L}{M}{R}$}
 $$
  D \isin C \equiv
   \begin{cases}
@@ -11,7 +11,7 @@ $$
     \text{as above with L and R exchanged}
   \end{cases}
 $$
-\proof{ ~ Truth table (ordered by original definition): \\
+\proof{ ~ Truth table (ordered by original definitions): \\
   \begin{tabular}{cccc|c|cc}
      $D = C$ &
           $\isin L$ &
@@ -175,12 +175,12 @@ $$
   \right]
  \implies
   \left[
-   \bigforall_{D \text{ s.t. } \isforeign{D}}
+   \bigforall_{D \in \foreign}
      D \isin C \equiv D \le C
   \right]
 $$
 \proof{
-Consider some $D$ s.t. $\isforeign{D}$.
+Consider some $D \in \foreign$.
 If $D = C$, trivially true.  For $D \neq C$,
 by Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
 And by Exact Ancestors $D \le L \equiv D \le C$.