diff --git a/APCCM2017_Stanger.tex b/APCCM2017_Stanger.tex
index e12f85a..43437a4 100644
--- a/APCCM2017_Stanger.tex
+++ b/APCCM2017_Stanger.tex
@@ -537,11 +537,11 @@
 
 %%%%%%%%%%%%%%%%%%%%
 
-As noted in Section~\ref{sec-relations-types}, any given value of \(S\!\) must comprise a subset of \(\TT{S}\), so the association between \(\T{S}\) and \(\TT{S}\) is total. Similarly, every tuple in \(\TT{S}\) must appear in at least one value of \(S\!\), so the association is also surjective. The association is neither functional nor injective, however, as a value of \(S\!\) in general may contain multiple tuples, and each tuple in \(\TT{S}\) can appear in multiple values of \(S\!\). This gives us \(\T{S}\SurTotal\TT{S}\).
+As discussed in Section~\ref{sec-relations-types}, any given value of \(S\!\) must comprise a subset of \(\TT{S}\), so the association between \(\T{S}\) and \(\TT{S}\) is total. Similarly, every tuple in \(\TT{S}\) must appear in at least one value of \(S\!\), so the association is also surjective. The association is neither functional nor injective, however, as a value of \(S\!\) in general may contain multiple tuples, and each tuple in \(\TT{S}\) can appear in multiple values of \(S\!\). This gives us \(\T{S}\SurTotal\TT{S}\).
     
-The key constraint on \Sno\ implies that the functional dependency \(\{\Sno\} \rightarrow \{\Sname, \Status, \City\}\) holds in \(S\!\). From equation \ref{eqn-tuple-type}, we can infer the type of \(\{\Sname, \Status, \City\}\) as \(\TSSC\). The association is functional and not injective by definition. As not every supplier number may appear in any given value of \(S\!\), there may be elements of \(\T{\Sno}\) that are not associated with an element of \(\TSSC\), and vice versa. This implies that the association is neither total nor surjective. This gives us \(\T{\Sno} \KeyEdge \TSSC\) (we introduce the label \(\mathit{key}\) to indicate that this edge represents a key constraint).
+The key constraint on \Sno\ implies that the functional dependency \(\{\Sno\} \rightarrow \{\Sname, \Status, \City\}\) holds in \(S\!\). From equation \ref{eqn-tuple-type}, we can infer the type of \(\{\Sname, \Status, \City\}\) as \(\TSSC\). The association is functional and not injective by definition. As not every supplier number may appear in any given value of \(S\!\), there may be elements of \(\T{\Sno}\) that are not associated with an element of \(\TSSC\), and vice versa. This implies that the association is neither total nor surjective. Indeed, this will be true for every edge that represents a key constraints. We introduce the edge label \(\mathit{key}\) to indicate that an edge represents a key constraint, which gives us \(\T{\Sno} \KeyEdge \TSSC\) in Figure~\ref{fig-sig-s-alone}. 
     
-Both \(\T{\Sno}\) and \(\TSSC\) are projections of \(\TT{S}\), so we can add (non-trivial) projection edges \(\TT{S} \ProjectionEdge \T{\Sname} \times \T{\Status} \times T_{\City}\) and \(\TT{S} \ProjectionEdge \T{\Sno}\). Similarly, \(\T{\Sname}\), \(\T{\Status}\), and \(\T{\City}\) are each projections of \(\TSSC\), so we can add further projection edges to these nodes, as shown in Figure~\ref{fig-sig-s-alone}.
+Both \(\T{\Sno}\) and \(\TSSC\) are projections of \(\TT{S}\), so we can add (non-trivial) projection edges \(\TT{S} \ProjectionEdge \T{\Sname} \times \T{\Status} \times T_{\City}\) and \(\TT{S} \ProjectionEdge \T{\Sno}\). Similarly, \(\T{\Sname}\), \(\T{\Status}\), and \(\T{\City}\) are all projections of \(\TSSC\), so we can add further projection edges to these nodes, as shown in Figure~\ref{fig-sig-s-alone}.
 
 Looking at Figure~\ref{fig-sig-s-alone}, it could be argued that the \(T_{\dots}\) type notation is redundant and unnecessarily complicates the diagram. Why not just use, e.g., \(S\!\) instead of \(\T{S}\), \(\Sno\) instead of \(\T{\Sno}\), and \(\Sno \times \Sname \times \Status \times \City\) instead of \(\TT{S}\)? It is important to remember, however, that SIGs like that shown in Figure~\ref{fig-sig-s-alone} include multiple elements of quite different kinds, including relations, tuples, and various combinations of attributes. Discarding the type notation might be reasonable in informal situations, but could lead to confusion between the different kinds of elements represented. The explicit type notation protects the semantics of the various elements of the schema and makes it clear what is being considered.