\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{t1\_topdim\_2 (TMG8QzJnsGwyrR1GSgEZXPwucJAKg8425iF)}
\maketitle
Let $ v7\_ordinal1 : {{\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\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_topdim\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_topdim\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}((r1\_xxreal\_0~k1\_xxreal\_0~X0){\unicdbdjdcd}(\\
X0=k1\_xxreal\_0))\end{array}
\label{hyp:ehedpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xreal\_0}~{k1\_xxreal\_0}}}}\label{hyp:ggdgcdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xxreal\_0~X2){\unicdbdjdcd}(((v1\_topdim\_2~X1~X0){\unicdbdjdcd}((\\
X2=k1\_topdim\_2~X0~X1){\unicdbdjded}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(((k1\_xxreal\_3~X2~np\_\_1 \in k1\_card\_1~X3){\unicdcdcdhd}(r1\_tarski~\\
X3~X1)){\unicdbdjdcd}(v1\_xboole\_0~(k6\_setfam\_1~X0~X3)))){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))){\unicdcdcdhd}((r1\_tarski~X3~X1){\unicdcdcdhd}((k1\_card\_1~\\
X3=k1\_xxreal\_3~X2~np\_\_1){\unicdcdcdhd}(\preoh (v1\_xboole\_0~(k6\_setfam\_1~X0~X3)){\unicdcdcdhd}\\
(\preoh v1\_xboole\_0~X3)))))))){\unicdcdcdhd}((\preoh v1\_topdim\_2~X1~X0){\unicdbdjdcd}((X2=k1\_topdim\_2~\\
X0~X1){\unicdbdjded}(X2=k1\_xxreal\_0)))))\end{array}
\label{hyp:egcdpfehpgahegjgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdpfehpgahegjgngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_topdim\_2~\\
X1~X2)~X0){\unicdbdjdcd}(v1\_topdim\_2~X2~X1)))\end{array}$$
\end{theorem}
\end{document}
