Index: /reasoner/reasoner.tex
===================================================================
--- /reasoner/reasoner.tex	(revision 62)
+++ /reasoner/reasoner.tex	(revision 63)
@@ -169,5 +169,5 @@
 As we will discuss in Section \ref{sectTranslation}, various constraints must be instantiated, complemented and rewritten during the constraint translation process, which is executed per project directly before the reasoning step in order to populate the constraint base. For this purpose, we use a specific notation indicating constraint creation combining algorithm elements carrying actual values/elements (written in mathematical notation) and IVML expression operation (stated in teletype) used to build up the constraint expression. For example, for creating the IVML constraint \IVML{x = 25;}, we denote in algorithms $\createConstraint{\IVML{assign(x, 25)}}$. The angle brackets indicate a constraint creation, the contents of the brackets the expression representing the constraint. Here, \IVML{assing} is the assign operation defined by IVML (actually implementing the equals in \IVML{x = 25;}), which returns a Boolean value indicating whether the execution of the operation succeeded. In an algorithm, we may denote $\createConstraint{\IVML{assign}(x, 25)}$, whereby $x$ is determined by the algorithm and used to generically describe a constraint instantiation. 
 
-As part of the constraint instantiation, variables must be replaced. Let $c=\createConstraint{\IVML{assign(x, 25)}}$ be a constraint and \IVML{y} be some IVML variable. Then $\varSubstitution{c}{x = y}$ leads to the substitution of all variables named \IVML{x} by \IVML{x}, i.e., for the example effectively to \IVML{y = 25}. If such substitutions are stored in a mapping, i.e., a set of $\mapEntry{e_s, e_t}$ with $e_s$ being the expression to be replaced and $e_t$ the replacing expression, we can apply this mapping to a constraint $c$ using $\varSubstitutionVarMapping{c}$. Moreover, we can combine a specific mapping and already stored mappings using $\varSubstitutionOtherVarMapping{c}{x = y}$. If the right side of a substitution is $\undef$, no substitution happens, e.g., in $\varSubstitution{c}{x = \undef}$.
+As part of the constraint instantiation, variables must be replaced. Let $c=\createConstraint{\IVML{assign(x, 25)}}$ be a constraint and \IVML{y} be some IVML variable. Then $\varSubstitution{c}{x = y}$ leads to the substitution of all variables named \IVML{x} by \IVML{x}, i.e., for the example effectively to \IVML{y = 25}. If such substitutions are stored in a mapping, i.e., a set of $\mapEntry{e_s, e_t}$ with $e_s$ being the expression to be replaced and $e_t$ the replacing expression, we can apply this mapping to a constraint $c$ using $\varSubstitutionVarMapping{c}$. Moreover, we can combine a specific mapping and already stored mappings using $\varSubstitutionOtherVarMapping{c}{x = y}$. Please note that such substitutions are transitive, i.e., if $\mapEntry{y}{z}\in \variableMapping$, $x$ will be replaced by $z$. If the right side of a substitution is $\undef$, no substitution happens, e.g., in $\varSubstitution{c}{x = \undef}$.
 
 For some purpose, the reasoning mechanism must classify constraints, in particular default value assignments over usual constraints. We indicate this information as a `$d$' in the constraint creation notation, i.e., for creating a default constraint, we denote $\createDefaultConstraint{\IVML{assign}(x, 25)}$
@@ -479,5 +479,5 @@
   \TBD{check isDerived(t)}\;
   $cs \assng \bigcup_{t \in allBase(t)} constraints(t)$\;
-  $add(\topLevelConstraints, \setWith{\createConstraint{\varSubstitution{c}{decl(c)=d}}}{c\in cs}, true)$\;
+  $add(\topLevelConstraints, \setWith{\createConstraint{\varSubstitutionOtherVarMapping{c}{decl(c)=d}}}{c\in cs}, true)$\;
  \caption{Translating constraints for derived types (\IVML{translateDerivedDatatypeConstraints}).}\label{algTranslateDerivedDatatypeConstraints}
 \end{algorithm}
@@ -491,5 +491,5 @@
 
   $cs \assng \bigcup_{t \in allBase(t} constraints(t)$\;
-  $add(\topLevelConstraints, \setWith{\createConstraint{\closedCases{d, & \text{if } ca = \undef \\ ca, &\text{else}}\rightarrow\IVML{forAll}(i|\text{ }\varSubstitution{c}{decl(c)=d})}}{c \in cs}, true)$\;
+  $add(\topLevelConstraints, \setWith{\createConstraint{\closedCases{d, & \text{if } ca = \undef \\ ca, &\text{else}}\rightarrow\IVML{forAll}(i|\text{ }\varSubstitutionOtherVarMapping{c}{decl(c)=d})}}{c \in cs}, true)$\;
  \caption{Translating constraints for derived container types (\IVML{translateContainerDerivedDatatypeConstraints}).}\label{algTranslateContainerDerivedDatatypeConstraints}
 \end{algorithm}