\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{t34\_topreala (TMZ4PfBpRkfxeuzxFkzfibxEPn4KcHijFCo)}
\maketitle
Let $ v3\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_topreala : {\iota}$ be given.
Let $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(u1\_struct\_0~(k2\_borsuk\_1~\\
k3\_topmetr~k3\_topmetr))~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}(\\
m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~\\
k3\_topmetr~k3\_topmetr))~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k1\_numbers){\unicdbdjdcd}(k1\_funct\_1~X0~(k4\_tarski~X1~X2)=k2\_finseq\_4~k1\_numbers~\\
X1~X2))){\unicdbdjdcd}(v3\_tops\_2~X0~(k2\_borsuk\_1~k3\_topmetr~k3\_topmetr)~(k15\_euclid~\\
np\_\_2)))\end{array}
\label{hyp:ehhdgdpfehpgahchfgbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k2\_finseq\_4~X0~X1~X2=k10\_finseq\_1~\\
X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_topreala){\unicdcdcdhd}((v1\_funct\_2~k2\_topreala~(u1\_struct\_0~\\
(k2\_borsuk\_1~k3\_topmetr~k3\_topmetr))~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~k2\_topreala~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~k3\_topmetr~k3\_topmetr))~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))))\end{array}
\label{hyp:egehpflgcdpfehpgahchfgbgmgbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(u1\_struct\_0~(k2\_borsuk\_1~\\
k3\_topmetr~k3\_topmetr))~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}(\\
m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~\\
k3\_topmetr~k3\_topmetr))~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}\\
((X0=k2\_topreala){\unicdbdjded}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(k1\_funct\_1~X0~(k4\_tarski~X1~X2)=k10\_finseq\_1~\\
X1~X2))))\end{array}
\label{hyp:egcdpfehpgahchfgbgmgbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddedpfehpgahchfgbgmgbg}
$$\begin{array}{c}v3\_tops\_2~k2\_topreala~(k2\_borsuk\_1~k3\_topmetr~k3\_topmetr)~(k15\_euclid~\\
np\_\_2)\end{array}$$
\end{theorem}
\end{document}
