\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{t74\_borsuk\_5 (TMHZ4AKrmCDVxfiCR8bZxC5PNt7LbSYVsn2)}
\maketitle
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_topmetr : {\iota}$ 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 $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k9\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_compts\_1~X0~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(u1\_struct\_0~k3\_topmetr)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}((X1=X0){\unicdbdjdcd}((v4\_xxreal\_2~X1){\unicdcdcdhd}(v3\_xxreal\_2~X1))))\end{array}
\label{hyp:ehhdddpfcgpgchdhfhlgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(k5\_seq\_4~\\
X0=k3\_seq\_4~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(k4\_seq\_4~\\
X0=k2\_seq\_4~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k3\_seq\_4}~{X0}})}})}}}\label{hyp:egehpflgddpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k2\_seq\_4}~{X0}})}})}}}\label{hyp:egehpflgcdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}((v3\_xxreal\_2~X0){\unicdbdjdcd}((v1\_xboole\_0~\\
X0){\unicdcdcdid}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((X1=k3\_seq\_4~X0){\unicdbdjded}(({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}((X2 \in X0){\unicdbdjdcd}(r1\_xxreal\_0~X1~X2))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(v1\_xreal\_0~X3){\unicdbdjdcd}(\preoh (X3 \in X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k9\_binop\_2~X1~X2)~X3))))))))))\end{array}
\label{hyp:egcdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}((v4\_xxreal\_2~X0){\unicdbdjdcd}((v1\_xboole\_0~\\
X0){\unicdcdcdid}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((X1=k2\_seq\_4~X0){\unicdbdjded}(({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}((X2 \in X0){\unicdbdjdcd}(r1\_xxreal\_0~X2~X1))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(v1\_xreal\_0~X3){\unicdbdjdcd}(\preoh (X3 \in X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X3~(k10\_binop\_2~X1~X2)))))))))))\end{array}
\label{hyp:egbdpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(v3\_membered~\\
X0)\end{array}
\label{hyp:dgdgidpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehhdedpfcgpgchdhfhlgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_compts\_1~X0~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(u1\_struct\_0~k3\_topmetr)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(((X2 \in X1){\unicdcdcdhd}(X1=X0)){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k5\_seq\_4~X1)~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k4\_seq\_4~X1))))))\end{array}$$
\end{theorem}
\end{document}
