Commit 7905c004 by Ralf Jung

### LaTeX: change \set macros

parent d7d3cacf
 ... ... @@ -249,7 +249,7 @@ Given a monoid $M$, we construct a monoid modeling someone owning an \emph{autho (If $M$ is an exclusive monoid, the construction is very similar to a half-ownership monoid with two asymmetric halves.) Let $\auth{M}$ be the monoid with carrier $\SET{ (x, \melt) }{ x \in \mcarp{\exm{\mcarp{M}}} \land \melt \in \mcarp{M} \land (x = \munit_{\exm{\mcarp{M}}} \lor \melt \leq_M x) } \setComp{ (x, \melt) }{ x \in \mcarp{\exm{\mcarp{M}}} \land \melt \in \mcarp{M} \land (x = \munit_{\exm{\mcarp{M}}} \lor \melt \leq_M x) }$ and multiplication ... ... @@ -341,7 +341,7 @@ We first lift the transition relation to \STSS \times \mathcal{P}(\STST) (impl \begin{align*} (s, T) \ra (s', T') \eqdef&\, s \ra s' \land \STSL(s) \uplus T = \STSL(s') \uplus T' \\ \textsf{frame}(s, T) \eqdef&\, (s, \STST \setminus (\STSL(s) \uplus T)) \\ \upclose(S, T) \eqdef&\, \SET{ s' \in \STSS}{\exists s \in S.\; \textsf{frame}(s, T) \ststrans \textsf{frame}(s', T) } \upclose(S, T) \eqdef&\, \setComp{ s' \in \STSS}{\exists s \in S.\; \textsf{frame}(s, T) \ststrans \textsf{frame}(s', T) } \end{align*} \noindent ... ... @@ -358,7 +358,7 @@ This is exactly what we have to show, since we know \STSL(s) \uplus T = \STSL(s Let \STSMon{\STSS} be the monoid with carrier \[ \SET{ (s, S, T) \in \exm{\STSS} \times \mathcal{P}(\STSS) \times \mathcal{P}(\STST) }{ \begin{aligned} &(s = \munit \lor s \in S) \land \upclose(S, T) = S \land{} \\& S \neq \emptyset \land \All s \in S. \STSL(s) \sep T \end{aligned} } \setComp{ (s, S, T) \in \exm{\STSS} \times \mathcal{P}(\STSS) \times \mathcal{P}(\STST) }{ \begin{aligned} &(s = \munit \lor s \in S) \land \upclose(S, T) = S \land{} \\& S \neq \emptyset \land \All s \in S. \STSL(s) \sep T \end{aligned} } and multiplication \[ ... ...
 ... ... @@ -152,9 +152,11 @@ \newcommand{\upclose}{\mathord{\uparrow}} \def\All #1.{\forall #1.\;}% \def\Exists #1.{\exists #1.\;}% \def\Ret #1.{#1.\;}% \newcommand{\spac}{\;} % a space \def\All #1.{\forall #1.\spac}% \def\Exists #1.{\exists #1.\spac}% \def\Ret #1.{#1.\spac}% \newcommand{\any}{{\rule[-.2ex]{1ex}{.4pt}}}% \newcommand{\unitval}{()}% ... ... @@ -182,21 +184,8 @@ \newcommand{\IF}{\mathrel{\text{if}}} \newcommand{\WHEN}{\textrm{when }} \newcommand{\SET}[2]{ \left\{% #1% \;\middle|\;% #2% \right\} } \newcommand{\SETB}[1]{ \left\{% #1% \right\} } \newcommand{\SETC}[2]{#1 & #2} \newcommand*\setComp[2]{\left\{#1\spac\middle|\spac#2\right\}} \newcommand*\set[1]{\left\{#1\right\}} \newenvironment{inbox}[1][]{ \begin{array}[#1]{@{}l@{}} ... ... @@ -317,8 +306,8 @@ %% various pieces of Syntax \newcommand{\unitsort}{1}% \unit is bold. \def\MU #1.{\mu #1.\;}% \def\Lam #1.{\lambda #1.\;}% \def\MU #1.{\mu #1.\spac}% \def\Lam #1.{\lambda #1.\spac}% \newcommand{\proves}{\vdash} \newcommand{\provesalways}{\vdash_{\!\!\boxempty}} ... ...
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