\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{t32\_borsuk\_6 (TMHHspcisj665NExMaDLPT1UAKyEGKwjQG1)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_borsuk\_1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_topmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
k5\_topmetr)){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}((\preoh \\
v1\_xboole\_0~(k8\_mcart\_1~k1\_numbers~k1\_numbers~(k1\_rcomp\_1~X0~\\
X1)~(k1\_rcomp\_1~X2~X3))){\unicdcdcdhd}((v2\_compts\_1~(k8\_mcart\_1~k1\_numbers~\\
k1\_numbers~(k1\_rcomp\_1~X0~X1)~(k1\_rcomp\_1~X2~X3))~(k2\_borsuk\_1~\\
k5\_topmetr~k5\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~(k8\_mcart\_1~k1\_numbers~\\
k1\_numbers~(k1\_rcomp\_1~X0~X1)~(k1\_rcomp\_1~X2~X3))~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~k5\_topmetr~k5\_topmetr))))))))))\end{array}
\label{hyp:ehjdpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X1~X2){\unicdbdjdcd}((v1\_xboole\_0~(k1\_rcomp\_1~\\
X1~X2)){\unicdcdcdhd}((v2\_compts\_1~(k1\_rcomp\_1~X1~X2)~X0){\unicdcdcdhd}(m1\_subset\_1~(k1\_rcomp\_1~\\
X1~X2)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:ehddbdpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_xboole\_0~k1\_xboole\_0){\unicdcdcdhd}((v2\_compts\_1~\\
k1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~k1\_xboole\_0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))\end{array}
\label{hyp:ehddadpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}(k8\_mcart\_1~\\
X0~X1~X2~X3=k2\_zfmisc\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_topmetr}={k17\_borsuk\_1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k17\_borsuk\_1){\unicdcdcdhd}((v1\_pre\_topc~k17\_borsuk\_1){\unicdcdcdhd}(\\
v2\_pre\_topc~k17\_borsuk\_1))\end{array}
\label{hyp:ggdgjdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}(v1\_xboole\_0~(k2\_zfmisc\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgedpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X1){\unicdbdjdcd}(v1\_xboole\_0~(k2\_zfmisc\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgddpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_topmetr}~{k17\_borsuk\_1}}\label{hyp:ggdgddpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}((v1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_pre\_topc~(k2\_borsuk\_1~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgcdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgbdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{l1\_pre\_topc}~{k17\_borsuk\_1}}\label{hyp:egehpflgbdhdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_topmetr~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdpfcgpgchdhfhlgpfgd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfcgpgchdhfhlgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~k5\_topmetr)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
k5\_topmetr)){\unicdbdjdcd}((v2\_compts\_1~(k8\_mcart\_1~k1\_numbers~k1\_numbers~\\
(k1\_rcomp\_1~X0~X1)~(k1\_rcomp\_1~X2~X3))~(k2\_borsuk\_1~k5\_topmetr~\\
k5\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~(k8\_mcart\_1~k1\_numbers~k1\_numbers~\\
(k1\_rcomp\_1~X0~X1)~(k1\_rcomp\_1~X2~X3))~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k2\_borsuk\_1~k5\_topmetr~k5\_topmetr))))))))\end{array}$$
\end{theorem}
\end{document}
