Rewritten first-order preliminaries

Chapters/Chapter03.tex

@@ -71,7 +71,7 @@ Q3B also uses \emph{destructive equality resolution} (\der) rule,
 which was proposed for quantified bit-vector formulas by Wintersteiger
 et al:
 \[
-  \forall x. \, (x \not = t ~\vee~ \varphi)~~\leadsto~~\varphi[x \leftarrow t],
+  \forall x. \, (x \not = t ~\vee~ \varphi[x])~~\leadsto~~\varphi[t],
 \]
 where $t$ is an arbitrary term that does not contain $x$. As the
 \der rule eliminates the quantified variable, it in many cases also
@@ -82,7 +82,7 @@ perform Skolemization before solving. Therefore we also need a dual
 version of the \der rule, which we have called \emph{constructive
   equality resolution}:
 \[
-  \exists x. \, (x = t ~\wedge~ \varphi)~~\leadsto~~\varphi[x \leftarrow t],
+  \exists x. \, (x = t ~\wedge~ \varphi[x])~~\leadsto~~\varphi[t],
 \]
 where $t$ is an arbitrary term that does not contain $x$.
 

Includes/notation.tex

@@ -19,6 +19,9 @@
 \newcommand{\mcbv}{\textsc{mcbv}\xspace}
 \newcommand{\nnf}{\textsc{nnf}\xspace}
 
+\newcommand{\true}{\ensuremath{\texttt{true}}}
+\newcommand{\false}{\ensuremath{\texttt{false}}}
+
 %solvers
 \newcommand{\uclid}{\textsc{uclid}\xspace}
 \newcommand{\fpacdcl}{\textsc{fp-acdcl}\xspace}
@@ -44,6 +47,7 @@
 \newcommand{\sort}[1]{\ensuremath{[#1]}}
 \newcommand{\extract}[2]{\ensuremath{\texttt{extract}^{#1}_{#2}}}
 
+
 \newcommand{\SymDivine}{\textsf{SymDIVINE}\xspace}
 
 \newcommand{\der}{\textsc{der}\xspace}