46 lines
1.1 KiB
TeX
46 lines
1.1 KiB
TeX
\documentclass{article}
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\usepackage{xspace}
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\usepackage{hyperref}
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\usepackage{bm}
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\usepackage[english]{babel}
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\usepackage{amsthm}
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\newcommand{\jh}[1]{{\leavevmode\color{blue!50!red}#1}}
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\input{notation.tex}
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\input{glossary.tex}
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\pagenumbering{arabic}
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\pagestyle{plain}
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\newtheorem{theorem}{Theorem}
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\begin{document}
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% \maketitle
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\definition{monotone}{define monotone}
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\definition{image}{define set image}
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\definition{completelattice}{define complete lattice}
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Hello world\cite{tarskilatticetheoretical1955}
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First, we generalize Knaster-Tarski Fixpoint Theorem.
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$$\fixpointsOf(S)$$
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\begin{theorem}[Tarski-Knaster Fixpoint Theorem~\cite{tarskilatticetheoretical1955}]
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For a \Monotone function $o$ over a \CompleteLattice $\langle \L, \lte \rangle$, we have that $\langle \fixpointsOf(o), \lte \rangle$ is a \CompleteLattice.
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\end{theorem}
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\begin{theorem}
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For a \Monotone function $o$ over a \CompleteLattice $\langle \L, \lte \rangle$, we have that $\langle o\imageNoLink{\L}, \lte \rangle$ is a \CompleteLattice.
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\end{theorem}
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\begin{proof}
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foo
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\end{proof}
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\bibliographystyle{plain}
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\bibliography{references}
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\end{document}
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