\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\_topdim\_1 (TMHs75HNvBz91mn3MgCFyX9KDi9qbZesNQY)}
\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\_topdim\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_topdim\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_topdim\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_topdim\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_topdim\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_real\_1 : {{\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 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}((((v2\_topdim\_1~X1~X0){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k3\_topdim\_1~X0~X1)~X2)){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~X2){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((X3 \in X1){\unicdbdjdcd}((v1\_topdim\_1~X3~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k2\_topdim\_1~X0~X3)~\\
X2)))))){\unicdcdcdhd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (\\
m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}((v1\_topdim\_1~\\
X3~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k2\_topdim\_1~X0~X3)~X2))))){\unicdbdjdcd}((v2\_topdim\_1~\\
X1~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_topdim\_1~X0~X1)~X2))))))\end{array}
\label{hyp:ehbdbdpfehpgahegjgngpfbd}
\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~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
(v1\_int\_1~(k3\_topdim\_1~X0~X1))\end{array}
\label{hyp:egehpflgddpfehpgahegjgngpfbd}
\end{equation}
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~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
((v2\_topdim\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_int\_1~X2){\unicdbdjdcd}((X2=k3\_topdim\_1~\\
X0~X1){\unicdbdjded}((r1\_tarski~X1~(k13\_prob\_1~(u1\_struct\_0~X0)~k5\_numbers~\\
(k9\_setfam\_1~(u1\_struct\_0~X0))~(k1\_topdim\_1~X0)~(k3\_real\_1~X2~\\
np\_\_1))){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (v1\_int\_1~\\
X3){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~X3){\unicdcdcdhd}(r1\_tarski~X1~(k13\_prob\_1~\\
(u1\_struct\_0~X0)~k5\_numbers~(k9\_setfam\_1~(u1\_struct\_0~X0))~(k1\_topdim\_1~\\
X0)~(k3\_real\_1~X3~np\_\_1)))){\unicdbdjdcd}(r1\_xxreal\_0~X2~X3)))))))))\end{array}
\label{hyp:eggdpfehpgahegjgngpfbd}
\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}
\begin{theorem}\label{thm:ehbdcdpfehpgahegjgngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(((v2\_topdim\_1~X1~X0){\unicdcdcdhd}(r1\_tarski~X2~X1)){\unicdbdjdcd}((v2\_topdim\_1~\\
X2~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_topdim\_1~X0~X2)~(k3\_topdim\_1~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
