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\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{definition}[theorem]{Definition}
\def\R{\mathbb{ R}}
\def\S{\mathbb{ S}}
\def\I{\mathbb{ I}}
\def\Scala{\texttt{Scala}}
\def\ScalaCheck{\texttt{ScalaCheck}}
\def\Haskell{\texttt{Haskell}}
\def\XML{\texttt{XML}}
\newcommand{\ldb}{[\![}
\newcommand{\rdb}{]\!]}
\newcommand{\ldrb}{(\!(}
\newcommand{\rdrb}{)\!)}
\newcommand{\lliftb}{\langle\!|}
\newcommand{\rliftb}{|\!\rangle}
\newcommand{\lrclr}{(\!*|}
\newcommand{\rrclr}{|\!*)}
\newcommand{\meaningof}[1]{\ldb #1 \rdb}
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