\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{t3\_tex\_4 (TMXQGgnx1YgYtr5RHvxw8ymMMcjne8ZXX3x)}
\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\_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 $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}(r1\_tarski~X2~X1)){\unicdbdjdcd}\\
(r1\_tarski~(k3\_tarski~X0)~X1)\end{array}
\label{hyp:ehhdgdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{r1\_tarski}~{X0}}~{({{k3\_tarski}~{X1}})}})}}}}\label{hyp:ehhdedpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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}(((v3\_pre\_topc~X1~X0){\unicdcdcdhd}(r1\_tarski~X1~X2)){\unicdbdjdcd}\\
(r1\_tarski~X1~(k1\_tops\_1~X0~X2)))))\end{array}
\label{hyp:ehcdedpfehpgahdhpfbd}
\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}(r1\_tarski~(k1\_tops\_1~X0~X1)~X1))\end{array}
\label{hyp:ehbdgdpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_pre\_topc~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}(k1\_tops\_1~X0~(k1\_tops\_1~X0~X1)=k1\_tops\_1~\\
X0~X1)\end{array}
\label{hyp:ahchpgkgfgdgehjgghjgehjhpflgbdpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(v3\_pre\_topc~\\
(k1\_tops\_1~X0~X1)~X0)\end{array}
\label{hyp:ggdgjdpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_pre\_topc~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k1\_tops\_1~X0~X1)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgbdpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddpfehfgihpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(k1\_tops\_1~X0~X1=k3\_tarski~(ReplSep~(toset~({\uniddcgcg} X2 : \iota .  \\
m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))~({\uniddcgcg} X2 : \iota .  \\
(v3\_pre\_topc~X2~X0){\unicdcdcdhd}(r1\_tarski~X2~X1))~({\uniddcgcg} X2 : \iota .  X2))))\end{array}$$
\end{theorem}
\end{document}
