\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{t56\_topgen\_1 (TMHYsoCi5pMwR2F6sDJPDBQaXUxbH64pouf)}
\maketitle
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 $ k3\_topmetr : {\iota}$ be given.
Let $ v2\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_borsuk\_5 : {\iota}$ be given.
Let $ k3\_numbers : {\iota}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_tops\_1~k1\_numbers~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~k1\_numbers~\\
(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr)))\end{array}
\label{hyp:ehfdfdpfehpgahhgfgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v2\_tops\_1~k1\_borsuk\_5~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~k1\_borsuk\_5~\\
(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr)))\end{array}
\label{hyp:ehfdedpfehpgahhgfgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v2\_tops\_1~k3\_numbers~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~k3\_numbers~(\\
k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr)))\end{array}
\label{hyp:ehfdddpfehpgahhgfgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_xboole\_0~X0~(k4\_xboole\_0~X1~X0)=k2\_xboole\_0~\\
X0~X1\end{array}
\label{hyp:ehddjdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k3\_topmetr}}={k1\_numbers}}\label{hyp:ehbdhdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{{k2\_xboole\_0}~{X0}}~{X1}}={X1}})}}}}\label{hyp:ehbdcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_tarski}~{k3\_numbers}}~{k1\_numbers}}\label{hyp:ehbdcdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_borsuk\_5}={{{k6\_subset\_1}~{k1\_numbers}}~{k3\_numbers}}}\label{hyp:egbdpfcgpgchdhfhlgpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfehpgahhgfgogpfbd}
$$\begin{array}{c}{\unicdcdaddd} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdcdcdhd}\\
({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdcdcdhd}\\
((v2\_tops\_1~X0~k3\_topmetr){\unicdcdcdhd}((v2\_tops\_1~X1~k3\_topmetr){\unicdcdcdhd}(\preoh v2\_tops\_1~\\
(k4\_subset\_1~(u1\_struct\_0~k3\_topmetr)~X0~X1)~k3\_topmetr))))\end{array}$$
\end{theorem}
\end{document}
