\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{t54\_borsuk\_5 (TMRzMqXvEe1nM14oneeWk1urxqkMPG6TTXo)}
\maketitle
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 $ k3\_topmetr : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((X0=k2\_rcomp\_1~X1~k1\_xxreal\_0){\unicdbdjdcd}\\
(k2\_pre\_topc~k3\_topmetr~X0=k3\_rcomp\_1~X1~k1\_xxreal\_0)))\end{array}
\label{hyp:ehedjdpfcgpgchdhfhlgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}((X0=\\
k3\_rcomp\_1~X1~X2){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(k2\_pre\_topc~k3\_topmetr~X0=k1\_rcomp\_1~\\
X1~X2)))))\end{array}
\label{hyp:ehddfdpfcgpgchdhfhlgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(k2\_pre\_topc~\\
X0~(k4\_subset\_1~(u1\_struct\_0~X0)~X1~X2)=k4\_subset\_1~(u1\_struct\_0~\\
X0)~(k2\_pre\_topc~X0~X1)~(k2\_pre\_topc~X0~X2))))\end{array}
\label{hyp:ehcdadpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k3\_topmetr}}={k1\_numbers}}\label{hyp:ehbdhdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~X1)){\unicdbdjdcd}(\\
k4\_subset\_1~k1\_numbers~(k1\_rcomp\_1~X0~X1)~(k3\_rcomp\_1~X2~k1\_xxreal\_0)=\\
k3\_rcomp\_1~X0~k1\_xxreal\_0))))\end{array}
\label{hyp:ehbdbdpfcgpgchdhfhlgpffd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{({{v2\_pre\_topc}~{k3\_topmetr}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{k3\_topmetr}})}}\label{hyp:egehpflgddpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k3\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgddpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgcdpfchdgpgngahpfbd}
\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~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdedpfcgpgchdhfhlgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}((X0=\\
k4\_subset\_1~k1\_numbers~(k3\_rcomp\_1~X1~X2)~(k2\_rcomp\_1~X2~k1\_xxreal\_0)){\unicdbdjdcd}\\
((r1\_xxreal\_0~X2~X1){\unicdcdcdid}(k2\_pre\_topc~k3\_topmetr~X0=k3\_rcomp\_1~X1~\\
k1\_xxreal\_0)))))\end{array}$$
\end{theorem}
\end{document}
