diff --git a/APCCM2017_Stanger.tex b/APCCM2017_Stanger.tex
index 749b24b..8fee155 100644
--- a/APCCM2017_Stanger.tex
+++ b/APCCM2017_Stanger.tex
@@ -712,28 +712,7 @@
 
 \noindent The SIG for \(\SC{1}\) will not just be that for relvar \(S\) (see Figure~\ref{fig-sig-s-alone}), as that schema did not incorporate all the constraints implicit in \(\SC{0}\). The process for constructing the SIG will be similar to that for the earlier example, however. The constraints appearing in \(\SC{1}\) are \Constraint{\ref{constraint-key}}(a), \Constraint[\SC{1}]{\ref{constraint-key}}(b), \Constraint[\SC{1}]{\ref{constraint-key}}(c), \Constraint[\SC{1}]{\ref{constraint-union}}--\Constraint[\SC{1}]{\ref{constraint-tuple-types}}, and \Constraint{\ref{constraint-implied-types-london}}--\Constraint{\ref{constraint-implied-types-TSSNL}}.
 
-The SIG will include all of the edges that appear in Figure~\ref{fig-sig-s-alone}. \(\T{S} \SurTotal \TT{S}\) implies \(\T{\LSsub} \SurTotal \TT{\LSsub}\) and \(\T{\NLSsub} \SurTotal \TT{\NLSsub}\). Constraints \Constraint{\ref{constraint-implied-types-london}}--\Constraint{\ref{constraint-implied-types-TSSNL}} imply the existence of several subtype nodes, plus corresponding selection and projection edges:
-% \begin{itemize}
-%    
-%     \item \(\TT{\LSsub} \ProjectionEdge \T{\Sno}\) and \(\TT{\NLSsub} \ProjectionEdge \T{\Sno}\)
-% 
-%     \item \(\TT{\LSsub} \ProjectionEdge \TSSL\)
-% 
-%     \item \(\TT{\NLSsub} \ProjectionEdge \TSSNL\)
-% 
-%     \item \(\TSSL \ProjectionEdge \T{\Sname}\)
-% 
-%     \item \(\TSSL \ProjectionEdge \T{\Status}\)
-% 
-%     \item \(\TSSL \ProjectionEdge\,\CityLondon\)
-% 
-%     \item \(\TSSNL \ProjectionEdge \T{\Sname}\)
-% 
-%     \item \(\TSSNL \ProjectionEdge \T{\Status}\)
-% 
-%     \item \(\TSSNL \ProjectionEdge \T{\City} \setminus \CityLondon\)
-% 
-% \end{itemize}
+The SIG will include all of the edges that appear in Figure~\ref{fig-sig-s-alone}. The constraints within the schema imply the existence of several subtype nodes (e.g., the two subtypes of \(\T{City}\) implied by \Constraint{\ref{constraint-implied-types-london}} and \Constraint{\ref{constraint-implied-types-nonlondon}}), along with corresponding selection and projection edges, which are listed in Table~\ref{Tab.SIG.Implied.Edges}. \Constraint[\SC{1}]{\ref{constraint-union}}, \Constraint[\SC{1}]{\ref{constraint-relation-type-union}}(a), and \Constraint[\SC{1}]{\ref{constraint-relation-type-union}}(b) are effectively tautologies that add no new information, and can thus be safely ignored. The completed SIG for \(\SC{1}\) is shown in Figure~\ref{fig-sig-s}.
 
 \begin{table*}
     \centering
@@ -742,13 +721,11 @@
         \textbf{Constraint}                                     &   \textbf{Implied edge(s)}    \\
         \midrule
         {\Constraint[\SC{1}]{\ref{constraint-key}}}(b)          &   \(\T{\Sno} \KeyEdge \TSSL\)   \\
-        {\Constraint[\SC{1}]{\ref{constraint-key}}}(c)          &   \(\T{\Sno} \KeyEdge \TSSNL\)   \\
+        \phantom{\Constraint[\SC{1}]{\ref{constraint-key}}}(c)  &   \(\T{\Sno} \KeyEdge \TSSNL\)   \\
         \midrule
-        {\Constraint[\SC{1}]{\ref{constraint-relation-types}}}  &   \(\T{S} \SelectionEdge \T{\LSsub}\)   \\
-            &   \(\TT{S} \SelectionEdge \TT{\LSsub}\)   \\
+        {\Constraint[\SC{1}]{\ref{constraint-relation-types}}}  &   \(\T{\LSsub} \SurTotal \TT{\LSsub}\) \quad\quad \(\T{S} \SelectionEdge \T{\LSsub}\) \quad\quad \(\TT{S} \SelectionEdge \TT{\LSsub}\)   \\
         \midrule
-        {\Constraint[\SC{1}]{\ref{constraint-tuple-types}}}     &   \(\T{S} \SelectionEdge \T{\NLSsub}\)   \\
-            &   \(\TT{S} \SelectionEdge \TT{\NLSsub}\)   \\
+        {\Constraint[\SC{1}]{\ref{constraint-tuple-types}}}     &   \(\T{\NLSsub} \SurTotal \TT{\NLSsub}\) \quad\quad \(\T{S} \SelectionEdge \T{\NLSsub}\) \quad\quad \(\TT{S} \SelectionEdge \TT{\NLSsub}\)   \\
         \midrule
         {\Constraint{\ref{constraint-implied-types-london}}}    &   \(\T{\City} \SelectionEdge \CityLondon\)   \\
         \midrule
@@ -767,39 +744,10 @@
             &   \(\TSSNL \ProjectionEdge \TCityMinusLondon\)  \\
         \bottomrule
     \end{tabular}
-    \caption{CAPTION.}
+    \caption{Constraints and the SIG edges they imply for schema \(\SC{1}\).}
     \label{Tab.SIG.Implied.Edges}
 \end{table*}
 
-% \Constraint[\SC{1}]{\ref{constraint-key}}(b) and \Constraint[\SC{1}]{\ref{constraint-key}}(c) imply two additional key edges:
-% \begin{itemize}
-%    
-%     \item \(\T{\Sno} \KeyEdge \TSSL\)
-% 
-%     \item \(\T{\Sno} \KeyEdge \TSSNL\)
-%    
-% \end{itemize}
-
-\Constraint[\SC{1}]{\ref{constraint-relation-type-union}}(a) implies node \(\TLSPlusNLSsub\) to represent \(\T{\LSsub} \RelUnion \T{\NLSsub}\). However, this node would be identical to \(\T{S}\), so we can ignore \Constraint[\SC{1}]{\ref{constraint-relation-type-union}}(a) and just continue to use \(\T{S}\). A similar argument applies for \Constraint[\SC{1}]{\ref{constraint-relation-type-union}}(b) and \(\TT{S}\).
-
-% \Constraint[\SC{1}]{\ref{constraint-relation-types}}--\Constraint[\SC{1}]{\ref{constraint-implied-types-TSSNL}} imply the following selection edges:
-% \begin{itemize}
-% 
-%     \item \(\T{S} \SelectionEdge \T{\LSsub}\) and \(\TT{S} \SelectionEdge \TT{\LSsub}\)
-%     
-%     \item \(\T{S} \SelectionEdge \T{\NLSsub}\) and \(\TT{S} \SelectionEdge \TT{\NLSsub}\)
-%     
-%     \item \(\T{\City} \SelectionEdge\,\CityLondon\)
-%     
-%     \item \(\T{\City} \SelectionEdge\,(\TCityMinusLondon)\)
-%     
-%     \item \(\TSSC \SelectionEdge\) \(\TSSL\)
-%     
-%     \item \(\TSSC \SelectionEdge \T{\Sname} \times \T{\Status} \times \T{\City} \setminus \CityLondon\)
-% 
-% \end{itemize}
-The complete SIG for \(\SC{1}\) is shown in Figure~\ref{fig-sig-s}.
-
 %%%%%%%%%%%%%%%%%%%%
 
 \begin{figure*}