strategy: define W in Notation

[topbloke-formulae.git] / lemmas.tex

diff --git a/lemmas.tex b/lemmas.tex
index 83fc3f69d6048a9446271e5e235bc3dcae792afc..8efa09c9bac137dcdca9e6d59531ec674128b1da 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}
 $$
-\proof{ ~ Truth table (ordered by original definition): \\
+\proof{ ~ Truth table (ordered by original definitions): \\
   \begin{tabular}{cccc|c|cc}
      $D = C$ &
           $\isin L$ &
@@ -175,19 +175,19 @@ $$
   \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 $D \le L \equiv D \le C$.
 So $D \isin C \equiv D \le C$.
 }
 
-\subsection{Totally Foreign Contents}
+\subsection{Totally Foreign Ancestry}
 Given conformant commits $A \in \set A$,
 $$
    \left[
@@ -206,6 +206,6 @@ $$
 \proof{
 Consider some $D \le C$.  If $D = C$, $\isforeign{D}$ trivially.
 If $D \neq C$ then $D \le A$ where $A \in \set A$.  By Foreign
-Contents of $A$, $\isforeign{D}$.
+Ancestry of $A$, $\isforeign{D}$.
 }