\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{t44\_tsep\_2 (TMPUEgMU7tK5sdCRwHv6gLMLFKZES6Q3kbk)}
\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 $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_tsep\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ r1\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\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}({\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}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_pre\_topc~X3~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X3))){\unicdbdjdcd}(\\
{\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(u1\_struct\_0~X3))){\unicdbdjdcd}(\\
((X4=X1){\unicdcdcdhd}(X5=X2)){\unicdbdjdcd}((r1\_connsp\_1~X0~X1~X2){\unicdbdjded}(r1\_connsp\_1~X3~X4~\\
X5))))))))\end{array}
\label{hyp:ehcdfdpfehdhfgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(m1\_subset\_1~(u1\_struct\_0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ehbdpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(l1\_pre\_topc~X1))\end{array}
\label{hyp:egehpfngbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_pre\_topc~X2~X0){\unicdbdjdcd}((r3\_tsep\_1~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((X3=u1\_struct\_0~\\
X1){\unicdcdcdhd}(X4=u1\_struct\_0~X2)){\unicdbdjdcd}(r1\_connsp\_1~X0~X3~X4)))))))\end{array}
\label{hyp:eggdpfehdhfgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehededpfehdhfgahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_pre\_topc~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_pre\_topc~X3~X0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_pre\_topc~X4~X1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_pre\_topc~X5~X1){\unicdbdjdcd}\\
(((u1\_struct\_0~X2=u1\_struct\_0~X4){\unicdcdcdhd}(u1\_struct\_0~X3=u1\_struct\_0~\\
X5)){\unicdbdjdcd}((r3\_tsep\_1~X0~X2~X3){\unicdbdjded}(r3\_tsep\_1~X1~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
