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\documentclass[11pt,a4paper,fleqn]{article}
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\usepackage{english}
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\usepackage{a4}
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\usepackage{bbb}
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\makeatletter
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%%% layout
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\sloppy
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\parindent 0pt
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\parskip 0.5ex
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%%% text mode
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\newcommand{\B}[1]{\textbf{#1}}
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\newcommand{\TT}[1]{\ifmmode\mbox{\texttt{#1}}\else\texttt{#1}\fi}
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\newcommand{\E}[1]{\emph{#1}}
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\renewcommand{\P}[1]{\textsc{#1}}
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\renewcommand{\labelenumi}{(\theenumi)}
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\newcommand{\dfn}[1]{{\bf #1}}
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\newcommand{\thy}[1]{\mbox{\sc #1}}
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%\newcommand{\thy}[1]{\mbox{\textsc{#1}}}
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\newcommand{\IHOL}{\thy{ihol}}
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\newcommand{\SIHOL}{\thy{sihol}}
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\newcommand{\HOL}{\thy{hol}}
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\newcommand{\HOLBB}{\thy{hol88}}
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\newcommand{\FOL}{\thy{fol}}
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\newcommand{\SET}{\thy{set}}
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\newcommand{\Pure}{\thy{Pure}}
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\newcommand{\secref}[1]{\S\ref{#1}}
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\newenvironment{matharray}[1]{\[\begin{array}{#1}}{\end{array}\]}
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%from alltt.sty
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\def\docspecials{\do\ \do\$\do\&%
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\do\#\do\^\do\^^K\do\_\do\^^A\do\%\do\~}
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\newenvironment{asc}{\small\trivlist \item[]\if@minipage\else\vskip\parskip\fi
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\leftskip\@totalleftmargin\rightskip\z@
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\parindent\z@\parfillskip\@flushglue\parskip\z@
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\@tempswafalse \def\par{\if@tempswa\hbox{}\fi\@tempswatrue\@@par}
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\obeylines \tt \catcode``=13 \@noligs \let\do\@makeother \docspecials
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\frenchspacing\@vobeyspaces}{\endtrivlist}
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\newenvironment{ascbox}{\vbox\bgroup\begin{asc}}{\end{asc}\egroup}
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\newcommand{\brk}{\end{ascbox}\vskip-20pt\begin{ascbox}}
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\newcommand{\out}[1]{{\fontfamily{cmtt}\fontseries{m}\fontshape{sl}\selectfont\ \ #1}}
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% warning environment
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\newcommand{\dbend}{\vtop to 0pt{\vss\hbox{\Huge\bf!}\vss}}
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\newenvironment{warning}{\medskip\medbreak\begingroup \clubpenalty=10000
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\noindent \hangindent1.5em \hangafter=-2
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\hbox to0pt{\hskip-\hangindent\dbend\hfill}\ignorespaces}%
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{\par\endgroup\medbreak}
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\newcommand{\Isa}{{\sc Isabelle}}
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\newcommand{\ML}{{\sc ml}}
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\newcommand{\Haskell}{{\rm Haskell}}
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\newcommand{\IMP}{"`$\Longrightarrow$"'}
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\newcommand{\PMI}{"`$\Longleftarrow$"'}
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%%% math mode
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%% generic defs
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\newcommand{\nquad}{\hskip-1em}
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\newcommand{\fct}[1]{\mathop{\rm #1}\nolimits}
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\newcommand{\idt}[1]{{\mathord{\it #1}}}
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\newcommand{\syn}[1]{{\mathord{\it #1}}}
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\newcommand{\text}[1]{\mbox{#1}}
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\newcommand{\rmtext}[1]{\mbox{\rm #1}}
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%\newcommand{\mtt}[1]{\mbox{\tt #1}}
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\newcommand{\falls}{\text{falls }}
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\newcommand{\sonst}{\text{sonst}}
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\newcommand{\Bool}{\bbbB}
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\newcommand{\Nat}{\bbbN}
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\newcommand{\Natz}{{\bbbN_0}}
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\newcommand{\Rat}{\bbbQ}
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\newcommand{\Real}{\bbbR}
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\newcommand{\dt}{{\mathpunct.}}
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\newcommand{\Gam}{\Gamma}
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\renewcommand{\epsilon}{\varepsilon}
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\renewcommand{\phi}{\varphi}
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\renewcommand{\rho}{\varrho}
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\newcommand{\eset}{{\{\}}}
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\newcommand{\etuple}{{\langle\rangle}}
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\newcommand{\dfneq}{\mathbin{\mathord:\mathord=}}
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\newcommand{\impl}{\Longrightarrow}
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\renewcommand{\iff}{{\;\;\mathord{\Longleftrightarrow}\;\;}}
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\newcommand{\dfniff}{{\;\;\mathord:\mathord{\Longleftrightarrow}\;\;}}
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\renewcommand{\land}{\mathrel{\,\wedge\,}}
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\renewcommand{\lor}{\mathrel{\,\vee\,}}
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\newcommand{\iso}{\cong}
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\newcommand{\union}{\cup}
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\newcommand{\sunion}{\mathbin{\;\cup\;}}
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\newcommand{\dunion}{\mathbin{\dot\union}}
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\newcommand{\Union}{\bigcup}
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\newcommand{\inter}{\cap}
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\newcommand{\where}{\mathrel|}
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\newcommand{\pto}{\rightharpoonup}
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\newcommand{\comp}{\circ}
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\newcommand{\aaast}{{\mathord*\mathord*\mathord*}}
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\newcommand{\all}[1]{\forall #1\dt\;}
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\newcommand{\ex}[1]{\exists #1\dt\;}
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\newcommand{\lam}[1]{\mathop{\lambda} #1\dt}
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\newcommand\lbrakk{\mathopen{[\![}}
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\newcommand\rbrakk{\mathclose{]\!]}}
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\newcommand{\unif}{\mathrel{=^?}}
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\newcommand{\notunif}{\mathrel{{\not=}^?}}
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\newcommand{\incompat}{\mathrel{\#}}
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%% specific defs
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\newcommand{\PLUS}{\mathord{\langle{+}\rangle}}
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\newcommand{\TIMES}{\mathord{\langle{*}\rangle}}
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% IHOL
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\newcommand{\TV}{\fct{TV}}
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\newcommand{\FV}{\fct{FV}}
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\newcommand{\BV}{\fct{BV}}
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\newcommand{\VN}{\fct{VN}}
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\newcommand{\AT}{\fct{AT}}
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\newcommand{\STV}{\fct{STV}}
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\newcommand{\TyVars}{\syn{TyVars}}
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\newcommand{\TyNames}{\syn{TyNames}}
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\newcommand{\TyCons}{\syn{TyCons}}
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\newcommand{\TyConsSg}{\TyCons_\Sigma}
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\newcommand{\Types}{\syn{Types}}
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\newcommand{\TypesSg}{\Types_\Sigma}
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\newcommand{\GrTypes}{\syn{GrTypes}}
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\newcommand{\GrTypesSg}{\GrTypes_\Sigma}
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\newcommand{\VarNames}{\syn{VarNames}}
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\newcommand{\Vars}{\syn{Vars}}
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\newcommand{\VarsSg}{\Vars_\Sigma}
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\newcommand{\GrVars}{\syn{GrVars}}
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\newcommand{\GrVarsSg}{\GrVars_\Sigma}
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\newcommand{\ConstNames}{\syn{ConstNames}}
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\newcommand{\Consts}{\syn{Consts}}
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\newcommand{\ConstsSg}{\Consts_\Sigma}
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\newcommand{\GrConsts}{\syn{GrConsts}}
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\newcommand{\GrConstsSg}{\GrConsts_\Sigma}
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\newcommand{\Terms}{\syn{Terms}}
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\newcommand{\TermsSg}{\Terms_\Sigma}
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\newcommand{\GrTerms}{\syn{GrTerms}}
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\newcommand{\GrTermsSg}{\GrTerms_\Sigma}
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\newcommand{\Forms}{\syn{Forms}}
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\newcommand{\FormsTh}{\Forms_\Theta}
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\newcommand{\Seqs}{\syn{Seqs}}
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\newcommand{\SeqsTh}{\Seqs_\Theta}
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\newcommand{\Axms}{\syn{Axms}}
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\newcommand{\AxmsTh}{\Axms_\Theta}
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\newcommand{\Thms}{\syn{Thms}}
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\newcommand{\ThmsTh}{\Thms_\Theta}
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\newcommand{\U}{{\cal U}}
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\newcommand{\UU}{\bbbU}
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\newcommand{\ty}{{\mathbin{\,:\,}}}
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\newcommand{\typ}[1]{{\mathord{\sl #1}}}
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\newcommand{\tap}{\mathord{\,}}
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\newcommand{\prop}{\typ{prop}}
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\newcommand{\itself}{\typ{itself}}
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\newcommand{\cnst}[1]{{\mathord{\sl #1}}}
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\newcommand{\ap}{\mathbin{}}
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\newcommand{\To}{\Rightarrow}
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\newcommand{\Eq}{\equiv}
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\newcommand{\Impl}{\Rightarrow}
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\newcommand{\Forall}{\mathop{\textstyle\bigwedge}}
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\newcommand{\All}[1]{\Forall #1\dt}
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\newcommand{\True}{\top}
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\newcommand{\False}{\bot}
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\newcommand{\Univ}{{\top\!\!\!\!\top}}
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\newcommand{\Conj}{\wedge}
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\newcommand{\TYPE}{\cnst{TYPE}}
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% rules
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\newcommand{\Axm}{\rmtext{Axm}}
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\newcommand{\Assm}{\rmtext{Assm}}
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\newcommand{\Mon}{\rmtext{Mon}}
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\newcommand{\ImplI}{\mathord{\Impl}\rmtext{I}}
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\newcommand{\ImplE}{\mathord{\Impl}\rmtext{E}}
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\newcommand{\ImplMP}{\rmtext{MP}}
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\newcommand{\ImplRefl}{\mathord{\Impl}\rmtext{Refl}}
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\newcommand{\ImplTrans}{\mathord{\Impl}\rmtext{Trans}}
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\newcommand{\EqRefl}{\mathord{\Eq}\rmtext{Refl}}
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\newcommand{\EqTrans}{\mathord{\Eq}\rmtext{Trans}}
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\newcommand{\EqSym}{\mathord{\Eq}\rmtext{Sym}}
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\newcommand{\EqApp}{\mathord{\Eq}\rmtext{App}}
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\newcommand{\EqAbs}{\mathord{\Eq}\rmtext{Abs}}
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\newcommand{\Eqa}{\mathord{\Eq}\alpha}
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\newcommand{\Eqb}{\mathord{\Eq}\beta}
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\newcommand{\Eqe}{\mathord{\Eq}\eta}
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\newcommand{\Ext}{\rmtext{Ext}}
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\newcommand{\EqI}{\mathord{\Eq}\rmtext{I}}
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\newcommand{\EqMP}{\mathord{\Eq}\rmtext{MP}}
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\newcommand{\EqUnfold}{\mathord{\Eq}\rmtext{Unfold}}
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\newcommand{\EqFold}{\mathord{\Eq}\rmtext{Fold}}
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\newcommand{\AllI}{\mathord{\Forall}\rmtext{I}}
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\newcommand{\AllE}{\mathord{\Forall}\rmtext{E}}
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\newcommand{\TypInst}{\rmtext{TypInst}}
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\newcommand{\Inst}{\rmtext{Inst}}
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\newcommand{\TrueI}{\True\rmtext{I}}
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\newcommand{\FalseE}{\False\rmtext{E}}
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\newcommand{\UnivI}{\Univ\rmtext{I}}
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\newcommand{\ConjI}{\mathord{\Conj}\rmtext{I}}
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\newcommand{\ConjE}{\mathord{\Conj}\rmtext{E}}
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\newcommand{\ConjProj}{\mathord{\Conj}\rmtext{Proj}}
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\newcommand{\ImplCurry}{\mathord{\Impl}\rmtext{Curry}}
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\newcommand{\ImplUncurry}{\mathord{\Impl}\rmtext{Uncurry}}
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\newcommand{\CImplI}{\mathord{\Conj}\mathord{\Impl}\rmtext{I}}
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\newcommand{\CImplE}{\mathord{\Conj}\mathord{\Impl}\rmtext{E}}
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\newcommand{\Subclass}{\rmtext{Subclass}}
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\newcommand{\Subsort}{\rmtext{Subsort}}
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\newcommand{\VarSort}{\rmtext{VarSort}}
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\newcommand{\Arity}{\rmtext{Arity}}
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\newcommand{\SortMP}{\rmtext{SortMP}}
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\newcommand{\TopSort}{\rmtext{TopSort}}
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\newcommand{\OfSort}{\rmtext{OfSort}}
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\newcommand{\infr}{{\mathrel/}}
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\newcommand{\einfr}{{}{\mathrel/}}
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\newcommand{\drv}{\mathrel{\vdash}}
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\newcommand{\Drv}[1]{\mathrel{\mathord{\drv}_{#1}}}
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\newcommand{\Gdrv}{\Gam\drv}
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\newcommand{\edrv}{\mathop{\drv}\nolimits}
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\newcommand{\Edrv}[1]{\mathop{\drv}\nolimits_{#1}}
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\newcommand{\notEdrv}[1]{\mathop{\not\drv}\nolimits_{#1}}
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\newcommand{\lsem}{\lbrakk}
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\newcommand{\rsem}{\rbrakk}
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\newcommand{\sem}[1]{{\lsem #1\rsem}}
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\newcommand{\vld}{\mathrel{\models}}
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\newcommand{\Vld}[1]{\mathrel{\mathord{\models}_#1}}
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\newcommand{\Evld}[1]{\mathop{\vld}\nolimits_{#1}}
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\newcommand{\notEvld}[1]{\mathop{\not\vld}\nolimits_{#1}}
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\newcommand{\EQ}{\fct{EQ}}
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\newcommand{\IMPL}{\fct{IMPL}}
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\newcommand{\ALL}{\fct{ALL}}
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\newcommand{\extcv}{\mathrel{\unlhd}}
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\newcommand{\weakth}{\preceq}
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\newcommand{\eqvth}{\approx}
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\newcommand{\extdcli}{\mathrel{<_{\rm dcl}^1}}
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\newcommand{\extdcl}{\mathrel{\le_{\rm dcl}}}
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\newcommand{\extdfni}{\mathrel{<_{\rm dfn}^1}}
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\newcommand{\extdfn}{\mathrel{\le_{\rm dfn}}}
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\newcommand{\extsdfn}{\mathrel{\le_{\rm sdfn}}}
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\newcommand{\extqdfn}{\mathrel{\le_{\rm qdfn}}}
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\newcommand{\lvarbl}{\langle}
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\newcommand{\rvarbl}{\rangle}
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\newcommand{\varbl}[1]{{\lvarbl #1\rvarbl}}
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\newcommand{\up}{{\scriptstyle\mathord\uparrow}}
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\newcommand{\down}{{\scriptstyle\mathord\downarrow}}
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\newcommand{\Down}{{\mathord\downarrow}}
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\newcommand{\Sle}{{\mathrel{\le_S}}}
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\newcommand{\Classes}{\syn{Classes}}
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\newcommand{\ClassNames}{\syn{ClassNames}}
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\newcommand{\Sorts}{\syn{Sorts}}
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\newcommand{\TyVarNames}{\syn{TyVarNames}}
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\newcommand{\STyVars}{\syn{STyVars}}
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\newcommand{\STyArities}{\syn{STyArities}}
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\newcommand{\STypes}{\syn{STypes}}
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\newcommand{\SVars}{\syn{SVars}}
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\newcommand{\SConsts}{\syn{SConsts}}
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\newcommand{\STerms}{\syn{STerms}}
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\newcommand{\SForms}{\syn{SForms}}
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\newcommand{\SAxms}{\syn{SAxms}}
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\newcommand{\T}{{\cal T}}
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\newcommand{\cls}[1]{{\mathord{\sl #1}}}
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\newcommand{\intsrt}{\sqcap}
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\newcommand{\Intsrt}{{\mathop\sqcap}}
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\newcommand{\subcls}{\preceq}
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\newcommand{\Subcls}[1]{\mathrel{\subcls_{#1}}}
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\newcommand{\subsrt}{\sqsubseteq}
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\newcommand{\Subsrt}[1]{\mathrel{\subsrt_{#1}}}
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\newcommand{\subsrtp}{\sqsubset}
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\newcommand{\eqvsrt}{\approx}
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\newcommand{\topsrt}{\top}
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\newcommand{\srt}{\ty}
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\newcommand{\sct}[1]{{\bf #1}}
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\newcommand{\CLASSES}{\sct{classes}}
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\newcommand{\CLASSREL}{\sct{classrel}}
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\newcommand{\TYPES}{\sct{types}}
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\newcommand{\ARITIES}{\sct{arities}}
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\newcommand{\CONSTS}{\sct{consts}}
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\newcommand{\AXIOMS}{\sct{axioms}}
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\newcommand{\DEFNS}{\sct{defns}}
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\newcommand{\AXCLASS}{\sct{axclass}}
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\newcommand{\INSTANCE}{\sct{instance}}
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\newcommand{\Srt}{{\mathbin{\,:\,}}}
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\newcommand{\insrt}[2]{{\mathopen{(\!|} #1 \Srt #2 \mathclose{|\!)}}}
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\newcommand{\ofsrt}[2]{{\mathopen{\langle\!|} #1 \Srt #2 \mathclose{|\!\rangle}}}
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\newcommand{\injV}{{\iota_V}}
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\newcommand{\inj}{\iota}
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\newcommand{\injC}{{\iota_C}}
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\newcommand{\I}{{\cal I}}
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\newcommand{\C}{{\cal C}}
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\newcommand{\Sdrv}{\mathrel{\vdash\!\!\!\vdash}}
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\newcommand{\SDrv}[1]{\mathrel{\mathord{\Sdrv}_{#1}}}
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\newcommand{\SGdrv}{\Gam\Sdrv}
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\newcommand{\Sedrv}{\mathop{\Sdrv}\nolimits}
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\newcommand{\SEdrv}[1]{\mathop{\Sdrv}\nolimits_{#1}}
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\newcommand{\SSubclass}{\rmtext{S-Subclass}}
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\newcommand{\SSubsort}{\rmtext{S-Subsort}}
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\newcommand{\SVarSort}{\rmtext{S-VarSort}}
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\newcommand{\SArity}{\rmtext{S-Arity}}
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\newcommand{\SSortMP}{\rmtext{S-SortMP}}
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\newcommand{\STopSort}{\rmtext{S-TopSort}}
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\newcommand{\SOfSort}{\rmtext{S-OfSort}}
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\makeatother
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