%questo e' il file mycmds.tex

\newcommand{\startclauses}{ \vspace{3mm} \\ \begin{math}
\begin{array}{llllll}}
\newcommand{\stopclauses}{\end{array} \end{math}
\vspace{3mm} \\}

\newcommand{\hsuno}{\hspace{ 1cm}}
        % spazio orizzontale piccolo
\newcommand{\vsuno}{\vspace{ .4cm}}
        % spazio verticale medio
\newcommand{\vszero}{\vspace{ .2cm}}
        % spazio verticale piccolo

\newcommand{\undefined}{{\em undefined}}
\newcommand{\true}{{\em true}}
\newcommand{\false}{{\em false}}
\newcommand{\follows}{{\em follows}}
\newcommand{\equivalent}{{\em equivalent}}
\newcommand{\delay}{{\em delay}}
\newcommand{\mthree}{\mbox{$\:\models_{\it HU}\:$}}

\newcommand{\IFF}{\mbox{\hspace{0.3cm}iff\hspace{0.3cm}}}
\newcommand{\COMP}[1]{\mbox{{\em Comp}$({#1})$}}
\newcommand{\KU}[1]{\mbox{{\em Kun}$({#1})$}}
\newcommand{\FIT}[1]{\mbox{{\em Fit}$({#1})$}}
\newcommand{\PHI}[2]{\mbox{$\Phi_{#1}^{#2}$}}
        % operatore di Fitting
\newcommand{\TEXC}[1]{\mbox{$ \exists X C $}}
\newcommand{\TEXQ}{\mbox{$ \exists X Q $}}
\newcommand{\TEYD}[1]{\mbox{$ \exists Y D $}}

%VECCHI
%\newcommand{\TEXoC}[1]{\mbox{$ \exists X_{#1} \widetilde{C}_{#1} $}}
%\newcommand{\TEYoD}[1]{\mbox{$ \exists Y_{#1} \wideetilde{D}_{#1} $}}
%\newcommand{\TEXoD}[1]{\mbox{$ \exists X_{#1} \widetilde{D}_{#1} $}}

\newcommand{\TEXoC}[1]{\mbox{$ \exists\,\tilde{x}_{#1}\:\tilde{C}_{#1} $}}
\newcommand{\TEYoD}[1]{\mbox{$ \exists\,\tilde{y}_{#1}\:\tilde{D}_{#1} $}}
\newcommand{\TEXoD}[1]{\mbox{$ \exists\,\tilde{x}_{#1}\:\tilde{D}_{#1} $}}


\newcommand{\FAIL}{{\bf fail}}
\newcommand{\ES}{\mbox{$\emptyset$}}    % remember this one

\newcommand{\Ra}{\mbox{$\:\Rightarrow\:$}}
\newcommand{\La}{\mbox{$\:\Leftarrow\:$}}
\newcommand{\Lra}{\mbox{$\:\Leftrightarrow\:$}}
\newcommand{\notRa}{\mbox{$\:\not\Rightarrow\:$}}
\newcommand{\la}{\mbox{$\:\leftarrow\:$}}
\newcommand{\ra}{\mbox{$\:\rightarrow\:$}}
\newcommand{\tra}{\mbox{$\:\rightarrow^*\:$}}
\newcommand{\lra}{\mbox{$\:\leftrightarrow\:$}}

\newcommand{\Or}{\mbox{$\ \vee\ $}}
\newcommand{\And}{\mbox{$\ \wedge\ $}}
\newcommand{\A}{\mbox{$\ \wedge\ $}}
\newcommand{\U}{\mbox{$\:\cup\:$}}
\newcommand{\I}{\mbox{$\:\cap\:$}}
\newcommand{\sse}{\mbox{$\:\subseteq\:$}}

\newcommand{\fa}{\mbox{$\forall$}}
\newcommand{\te}{\mbox{$\exists$}}
\newcommand{\fai}{\mbox{$\stackrel{\infty}{\forall}$}}
\newcommand{\tei}{\mbox{$\stackrel{\infty}{\exists}$}}

\newcommand{\LLn}{\mbox{$1,\ldots,n$}}
\newcommand{\LL}{\mbox{$\ldots$}}

\newcommand{\D}[1]{\mbox{$|[{#1}]|$}}           % |[ ]| braces
\newcommand{\B}[1]{\mbox{$[\![{#1}]\!]$}}               % brackets
\newcommand{\C}[1]{\mbox{$\{{#1}\}$}}           % curly braces

\newcommand{\NI}{\noindent}
\newcommand{\HB}{\hfill{$\Box$}}
\newcommand{\VV}{\vspace{5 mm}}  % sono vecchi ma li ho tenuti
\newcommand{\III}{\vspace{3 mm}}   % sono vecchi ma li ho tenuti
\newcommand{\II}{\vspace{2 mm}}

\newcommand{\X}[1]{\mbox{$\:\stackrel{{#1}}{\rightarrow}\:$}}
\newcommand{\lX}[1]{\mbox{$\:\stackrel{{#1}}
                                                {\longrightarrow}\:$}}

%simboli usati in formule si usa \S+lettera/e che serve

%NUOVI
\newcommand{\lll}{{\cal L}}

\newcommand{\lfp}{\mbox{\it lfp}}

\newcommand{\eqdef}{\stackrel {\rm def}{=}}

\newcommand{\ol}[1]{\mbox{$\tilde{#1}$}}

%VECCHI
%\newcommand{\oA}{\mbox{$\widetilde{A}$}}
%\newcommand{\oB}{\mbox{$\widetilde{B}$}}
%\newcommand{\oC}{\mbox{$\widetilde{C}$}}
%\newcommand{\oD}{\mbox{$\widetilde{D}$}}
%\newcommand{\oE}{\mbox{$\widetilde{E}$}}
%\newcommand{\oF}{\mbox{$\widetilde{F}$}}
%\newcommand{\oG}{\mbox{$\widetilde{G}$}}
%\newcommand{\oH}{\mbox{$\widetilde{H}$}}
%\newcommand{\oJ}{\mbox{$\widetilde{J}$}}
%\newcommand{\oK}{\mbox{$\widetilde{K}$}}
%\newcommand{\oL}{\mbox{$\widetilde{L}$}}
%\newcommand{\oR}{\mbox{$\widetilde{K}$}}
%\newcommand{\oS}{\mbox{$\widetilde{L}$}}
%\newcommand{\oX}{\mbox{$\widetilde{X}$}}
%\newcommand{\oY}{\mbox{$\widetilde{Y}$}}
%\newcommand{\oW}{\mbox{$\widetilde{W}$}}
%
%\newcommand{\ot}{\mbox{$\widetilde{t}$}}
%
%
%\newcommand{\oKpr}{\mbox{$\widetilde{K'}$}}


\newcommand{\oA}{\mbox{$\tilde{A}$}}
\newcommand{\oB}{\mbox{$\tilde{B}$}}
\newcommand{\oC}{\mbox{$\tilde{C}$}}
\newcommand{\oD}{\mbox{$\tilde{D}$}}
\newcommand{\oE}{\mbox{$\tilde{E}$}}
\newcommand{\oF}{\mbox{$\tilde{F}$}}
\newcommand{\oG}{\mbox{$\tilde{G}$}}
\newcommand{\oH}{\mbox{$\tilde{H}$}}
\newcommand{\oJ}{\mbox{$\tilde{J}$}}
\newcommand{\oK}{\mbox{$\tilde{K}$}}
\newcommand{\oL}{\mbox{$\tilde{L}$}}
\newcommand{\oR}{\mbox{$\tilde{K}$}}
\newcommand{\oS}{\mbox{$\tilde{L}$}}
\newcommand{\oX}{\mbox{$\tilde{X}$}}
\newcommand{\oY}{\mbox{$\tilde{Y}$}}
\newcommand{\oW}{\mbox{$\tilde{W}$}}

\newcommand{\ot}{\mbox{$\tilde{t}$}}

\newcommand{\oKpr}{\mbox{$\tilde{K'}$}}


\newcommand{\NL}{\mbox{}\\}

\newcommand{\DCA}{\mbox{DCA$_{\cal L}$}}
\newcommand{\WDCA}{\mbox{WDCA$_{\cal L}$}}

\newcommand{\precdca}{\:\preceq_{{\cal T}^{\cal L}_1(P)}\:}
\newcommand{\equivdca}{\:\cong_{{\cal T}^{\cal L}_1(P)}\:}

\newcommand{\precprog}[2]{\:\preceq_{{\cal T}^{\cal L}_{#1}(#2)}\:}
\newcommand{\equiprog}[2]{\:\cong_{{\cal T}^{\cal L}_{#1}(#2)}\:}

%\newcommand{\precdca}{\:\preceq_{Comp_{\cal L}(P) \: \cup \:{\rm DCA}_{\cal L}}\:}
%\newcommand{\equivdca}{\:\cong_{Comp_{\cal L}(P) \:\cup\: {\rm DCA}_{\cal L}}\:}

%\newcommand{\precdcaa}[1]{\:\preceq_{Comp_{\cal L}(#1) \: \cup \:{\rm DCA}_{\cal L}}\:}
%\newcommand{\equivdcaa}[1]{\:\cong_{Comp_{\cal L}(#1) \:\cup\: {\rm DCA}_{\cal L}}\:}

%\newcommand{\precwdca}{\:\preceq_{Comp_{\cal L}(P) \:\cup\: {\rm WDCA}_{\cal L}}\:}
%\newcommand{\equivwdca}{\:\cong_{Comp_{\cal L}(P) \:\cup\: {\rm WDCA}_{\cal L}}\:}

\newcommand{\precinf}{\:\preceq_{Comp_{\cal L}(P)}\:}
\newcommand{\equivinf}{\:\cong_{Comp_{\cal L}(P)}\:}

\newcommand{\VAR}{\mbox{\it Var}}
\newcommand{\FV}{\mbox{\it FV}}

\newcommand{\T}{{\cal T}^{\cal L}}

%AGGIUNTI, APRILE 1995
\newcommand{\var}{{\it Var}}
\newcommand{\dom}{{\it Dom}}
\newcommand{\Var}{{\it Var}}
\newcommand{\Dom}{{\it Dom}}
\newcommand{\Range}{{\it Range}}
\newcommand{\range}{{\it Ran}}
\newcommand{\vect}[1]{{\bf #1}}
