\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t22\_nagata\_2 (TMQ6RSfhfKH4tbztk8UXjBocLVCvq9DNRqx)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_nagata\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_pcomps\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_nagata\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_nagata\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_nagata\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nagata\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_cantor\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(\preoh (v3\_pcomps\_1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))))){\unicdbdjdcd}(\preoh v5\_nagata\_1~X1~X0)))\end{array}
\label{hyp:ehcdbdpfogbghgbgehbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(((v9\_pre\_topc~X0){\unicdcdcdhd}((v7\_pre\_topc~X0){\unicdcdcdhd}({\unicdcdaddd} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))))){\unicdcdcdhd}(v6\_nagata\_1~\\
X1~X0)))){\unicdbdjded}(v3\_pcomps\_1~X0))\end{array}
\label{hyp:ehbdjdpfogbghgbgehbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))))){\unicdbdjdcd}((v2\_nagata\_1~X1~X0){\unicdbdjdcd}(v3\_nagata\_1~X1~\\
X0)))\end{array}
\label{hyp:ehbdcdpfogbghgbgehbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))))))){\unicdbdjdcd}(m1\_subset\_1~(k2\_nagata\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgcdpfogbghgbgehbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))))){\unicdbdjdcd}((v6\_nagata\_1~X1~X0){\unicdbdjded}((v3\_nagata\_1~\\
X1~X0){\unicdcdcdhd}((v1\_tops\_2~(k2\_nagata\_1~X0~X1)~X0){\unicdcdcdhd}((v1\_cantor\_1~(k2\_nagata\_1~\\
X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_nagata\_1~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))))))\end{array}
\label{hyp:eggdpfogbghgbgehbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))))){\unicdbdjdcd}((v5\_nagata\_1~X1~X0){\unicdbdjded}((v2\_nagata\_1~\\
X1~X0){\unicdcdcdhd}((v1\_tops\_2~(k2\_nagata\_1~X0~X1)~X0){\unicdcdcdhd}((v1\_cantor\_1~(k2\_nagata\_1~\\
X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_nagata\_1~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))))))\end{array}
\label{hyp:egfdpfogbghgbgehbgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfogbghgbgehbgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(((v9\_pre\_topc~X0){\unicdcdcdhd}((v7\_pre\_topc~X0){\unicdcdcdhd}({\unicdcdaddd} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))))){\unicdcdcdhd}(v5\_nagata\_1~\\
X1~X0)))){\unicdbdjded}(v3\_pcomps\_1~X0))\end{array}$$
\end{theorem}
\end{document}
