\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{t12\_tops\_3 (TMEnV2HyWt7sV3ddMY1WQJoRRCyMBHVvyzK)}
\maketitle
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 $ v2\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_struct\_0 : {{\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 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v2\_tops\_1~\\
X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(((r1\_tarski~X2~X1){\unicdcdcdhd}(v3\_pre\_topc~X2~X0)){\unicdbdjdcd}(X2=k1\_xboole\_0)))))\end{array}
\label{hyp:ehfdadpfehpgahdhpfbd}
\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}(((X1=k2\_struct\_0~X0){\unicdbdjdcd}(k3\_subset\_1~(u1\_struct\_0~\\
X0)~X1=k1\_struct\_0~X0)){\unicdcdcdhd}(((k3\_subset\_1~(u1\_struct\_0~X0)~X1=k1\_struct\_0~\\
X0){\unicdbdjdcd}(X1=k2\_struct\_0~X0)){\unicdcdcdhd}(((X1=u1\_struct\_0~X0){\unicdbdjdcd}(k3\_subset\_1~\\
(u1\_struct\_0~X0)~X1=k1\_xboole\_0)){\unicdcdcdhd}((k3\_subset\_1~(u1\_struct\_0~\\
X0)~X1=k1\_xboole\_0){\unicdbdjdcd}(X1=u1\_struct\_0~X0))))))\end{array}
\label{hyp:ehcdpfehpgahdhpfdd}
\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}(((X1=k1\_struct\_0~X0){\unicdbdjdcd}(k3\_subset\_1~(u1\_struct\_0~\\
X0)~X1=k2\_struct\_0~X0)){\unicdcdcdhd}(((k3\_subset\_1~(u1\_struct\_0~X0)~X1=k2\_struct\_0~\\
X0){\unicdbdjdcd}(X1=k1\_struct\_0~X0)){\unicdcdcdhd}(((X1=k1\_xboole\_0){\unicdbdjdcd}(k3\_subset\_1~\\
(u1\_struct\_0~X0)~X1=u1\_struct\_0~X0)){\unicdcdcdhd}((k3\_subset\_1~(u1\_struct\_0~\\
X0)~X1=u1\_struct\_0~X0){\unicdbdjdcd}(X1=k1\_xboole\_0))))))\end{array}
\label{hyp:ehbdpfehpgahdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}((r1\_tarski~X1~X2){\unicdbdjded}(r1\_tarski~\\
(k3\_subset\_1~X0~X2)~(k3\_subset\_1~X0~X1))))\end{array}
\label{hyp:ehbdcdpfdhfhcgdhfgehpfbd}
\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 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k3\_subset\_1~\\
X0~(k3\_subset\_1~X0~X1)=X1)\end{array}
\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgddpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v3\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}(v4\_pre\_topc~(k3\_subset\_1~(u1\_struct\_0~X0)~X1)~X0)\end{array}
\label{hyp:ggdgddpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v4\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}(v3\_pre\_topc~(k3\_subset\_1~(u1\_struct\_0~X0)~X1)~X0)\end{array}
\label{hyp:ggdgcdpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k3\_subset\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgddpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfehpgahdhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v2\_tops\_1~\\
X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(((r1\_tarski~(k3\_subset\_1~(u1\_struct\_0~X0)~X1)~X2){\unicdcdcdhd}(v4\_pre\_topc~\\
X2~X0)){\unicdbdjdcd}(X2=u1\_struct\_0~X0)))))\end{array}$$
\end{theorem}
\end{document}
