\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t9\_nagata\_2 (TMa47aSskuZAuUErkhRP3RkYGEYCUrwGr9c)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_pcomps\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_nagata\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~k1\_numbers))))){\unicdbdjdcd}((r1\_nagata\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~X0){\unicdbdjdcd}((k1\_metric\_1~X0~X0~X1~X2~X2=k6\_numbers){\unicdcdcdhd}(\\
(k1\_metric\_1~X0~X0~X1~X2~X3=k1\_metric\_1~X0~X0~X1~X3~X2){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k1\_metric\_1~X0~X0~X1~X2~X4)~(k7\_real\_1~(k1\_metric\_1~X0~X0~X1~X2~X3)~\\
(k1\_metric\_1~X0~X0~X1~X3~X4)))))))))\end{array}
\label{hyp:mgedfdpfogbghgbgehbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~k1\_numbers))))){\unicdbdjdcd}((r1\_pcomps\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~X0){\unicdbdjdcd}(((k1\_metric\_1~X0~X0~X1~X2~X3=k6\_numbers){\unicdbdjdcd}\\
(X2=X3)){\unicdcdcdhd}(((X2=X3){\unicdbdjdcd}(k1\_metric\_1~X0~X0~X1~X2~X3=k6\_numbers)){\unicdcdcdhd}\\
((k1\_metric\_1~X0~X0~X1~X2~X3=k1\_metric\_1~X0~X0~X1~X3~X2){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k1\_metric\_1~X0~X0~X1~X2~X4)~(k7\_real\_1~(k1\_metric\_1~X0~X0~X1~X2~X3)~\\
(k1\_metric\_1~X0~X0~X1~X3~X4))))))))))\end{array}
\label{hyp:eggdpfahdgpgngahdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfogbghgbgehbgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~k1\_numbers))))){\unicdbdjdcd}((r1\_pcomps\_1~X0~X1){\unicdbdjdcd}(r1\_nagata\_1~\\
X0~X1))\end{array}$$
\end{theorem}
\end{document}
