\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{t11\_topalg\_2 (TMRmBtNTUPXJkupToFHuLiJkLoDD3e9ycoJ)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_topmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_topalg\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_topalg\_2 : {\iota}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjdcd}(v2\_topalg\_2~(k4\_topmetr~X0~X1))))\end{array}
\label{hyp:ehjdpfehpgahbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_topalg\_2}={k3\_topmetr}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfehpgahbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}((\preoh \\
v2\_struct\_0~(k4\_topmetr~X0~X1)){\unicdcdcdhd}((v1\_pre\_topc~(k4\_topmetr~X0~\\
X1)){\unicdcdcdhd}(m1\_pre\_topc~(k4\_topmetr~X0~X1)~k3\_topmetr)))\end{array}
\label{hyp:egehpflgedpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_pre\_topc~X0~k2\_topalg\_2){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}\\
(v2\_topalg\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v1\_borsuk\_2~X0)))\end{array}
\label{hyp:dgdgddpfehpgahbgmghgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfehpgahbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjdcd}(v1\_borsuk\_2~(k4\_topmetr~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
