\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=}
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\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{t31\_borsuk\_4 (TMUoRdpDmH4jXBxxhLMKLLZXUt4gkFzo4BL)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_measure5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_borsuk\_1 : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_connsp\_1~X0~k5\_topmetr){\unicdcdcdhd}\\
((v2\_compts\_1~X0~k5\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
k5\_topmetr)))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers))))\end{array}
\label{hyp:ehddadpfcgpgchdhfhlgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}((X0 \in k1\_xxreal\_1~X1~X2){\unicdbdjded}((r1\_xxreal\_0~X1~X0){\unicdcdcdhd}\\
(r1\_xxreal\_0~X0~X2)))))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}(v2\_measure5~X0)){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdcdcdhd}((r1\_xxreal\_0~X1~X2){\unicdcdcdhd}\\
(X0=k1\_rcomp\_1~X1~X2)))))\end{array}
\label{hyp:ehbdedpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k1\_rcomp\_1~\\
X0~X1=k1\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}((v2\_measure5~\\
X0){\unicdbdjded}({\unicdcdaddd} X1 .  (v1\_xreal\_0~X1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (v1\_xreal\_0~X2){\unicdcdcdhd}\\
(X0=k1\_rcomp\_1~X1~X2))))\end{array}
\label{hyp:egddpfngfgbgdhfhchfgfd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdedpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfcgpgchdhfhlgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_connsp\_1~X0~k5\_topmetr){\unicdcdcdhd}\\
((v2\_compts\_1~X0~k5\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
k5\_topmetr)))))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}((r1\_xxreal\_0~\\
X1~X2){\unicdcdcdhd}(X0=k1\_rcomp\_1~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
