\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{t19\_nagata\_1 (TML29PY35jbdJy1zSGoYQCko1SJeUPBZewL)}
\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 $ 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 $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nagata\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_cantor\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_tops\_2~X1~X0){\unicdcdcdhd}((v1\_cantor\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v3\_pre\_topc~X2~X0){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X3 \in X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(\preoh (X4 \in X1){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(r1\_tarski~\\
X4~X2)))))))))\end{array}
\label{hyp:ehddbdpfjhfgmgmgpghhpfjd}
\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){\unicdbdjded}({\unicdcdadad} X1 .  ((v3\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v3\_pre\_topc~X3~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (X2 \in \\
X3){\unicdcdcdhd}(r1\_tarski~(k2\_pre\_topc~X0~X3)~X1)))))))\end{array}
\label{hyp:ehcdbdpffhchjhdhpgigogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((r1\_tarski~X1~X2){\unicdbdjdcd}(r1\_tarski~(k2\_pre\_topc~\\
X0~X1)~(k2\_pre\_topc~X0~X2)))))\end{array}
\label{hyp:ehbdjdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfogbghgbgehbgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v9\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))))){\unicdbdjdcd}(((v1\_tops\_2~(k2\_nagata\_1~\\
X0~X1)~X0){\unicdcdcdhd}((v1\_cantor\_1~(k2\_nagata\_1~X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
(k2\_nagata\_1~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (v3\_pre\_topc~\\
X2~X0){\unicdcdcdhd}((X3 \in X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(\preoh (X3 \in X4){\unicdcdcdhd}((r1\_tarski~(k2\_pre\_topc~X0~X4)~X2){\unicdcdcdhd}(X4 \in k2\_nagata\_1~\\
X0~X1)))))))))))\end{array}$$
\end{theorem}
\end{document}
