\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{t21\_urysohn3 (TMJJ7pY2GMgB6M38LdHiBgdEkMjNfRmGtQS)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compts\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\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 $ k3\_topmetr : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v10\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v10\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_pre\_topc~\\
X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (r1\_xboole\_0~\\
X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}\\
(\preoh (v5\_pre\_topc~X3~X0~k3\_topmetr){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(k1\_seq\_1~X3~X4)){\unicdcdcdhd}\\
((r1\_xxreal\_0~(k1\_seq\_1~X3~X4)~np\_\_1){\unicdcdcdhd}(((X4 \in X1){\unicdbdjdcd}(k1\_seq\_1~X3~\\
X4=k6\_numbers)){\unicdcdcdhd}((X4 \in X2){\unicdbdjdcd}(k1\_seq\_1~X3~X4=np\_\_1)))))))))))\end{array}
\label{hyp:ehcdadpffhchjhdhpgigogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}((v8\_pre\_topc~X0){\unicdcdcdhd}(v1\_compts\_1~X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}\\
((v2\_pre\_topc~X0){\unicdcdcdhd}((v9\_pre\_topc~X0){\unicdcdcdhd}((v10\_pre\_topc~X0){\unicdcdcdhd}(v6\_waybel\_3~\\
X0))))))\end{array}
\label{hyp:dgdghdpfhhbgjhcgfgmgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpffhchjhdhpgigogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v8\_pre\_topc~\\
X0){\unicdcdcdhd}((v1\_compts\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_pre\_topc~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v4\_pre\_topc~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(\preoh (r1\_xboole\_0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(\\
(v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}\\
(\preoh (v5\_pre\_topc~X3~X0~k3\_topmetr){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(k1\_seq\_1~X3~X4)){\unicdcdcdhd}\\
((r1\_xxreal\_0~(k1\_seq\_1~X3~X4)~np\_\_1){\unicdcdcdhd}(((X4 \in X1){\unicdbdjdcd}(k1\_seq\_1~X3~\\
X4=k6\_numbers)){\unicdcdcdhd}((X4 \in X2){\unicdbdjdcd}(k1\_seq\_1~X3~X4=np\_\_1)))))))))))\end{array}$$
\end{theorem}
\end{document}
