\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\_borsuk\_1 (TMVvrsQCgfunbXkmWqmTESb7DYSaRkxcsip)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_eqrel\_1 : {{\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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_eqrel\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k1\_zfmisc\_1~X0)~X1){\unicdbdjdcd}((X2 \in X3){\unicdbdjdcd}(X3=k3\_funct\_2~\\
X0~X1~(k13\_eqrel\_1~X0~X1)~X2)))))\end{array}
\label{hyp:ehgdfdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_eqrel\_1~X2~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((\preoh X3 \in u1\_struct\_0~\\
X1){\unicdbdjdcd}(k6\_domain\_1~(u1\_struct\_0~X0)~X3 \in k13\_borsuk\_1~X0~X1~X2)))))\end{array}
\label{hyp:ehddcdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))\end{array}
\label{hyp:egehpfngbdpffgbhchfgmgpfbd}
\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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_eqrel\_1~X1~X0))){\unicdbdjdcd}((v1\_funct\_1~(k13\_eqrel\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k13\_eqrel\_1~X0~X1)~X0~X1){\unicdcdcdhd}(m1\_subset\_1~(k13\_eqrel\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))))\end{array}
\label{hyp:egehpflgbdddpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~\\
X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_eqrel\_1~X2~(u1\_struct\_0~X1))))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k13\_borsuk\_1~X0~X1~X2)){\unicdcdcdhd}(m1\_eqrel\_1~(k13\_borsuk\_1~\\
X0~X1~X2)~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgbdddpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_eqrel\_1~X1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v1\_funct\_1~(k12\_borsuk\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k12\_borsuk\_1~\\
X0~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k11\_borsuk\_1~X0~X1))){\unicdcdcdhd}((\\
v5\_pre\_topc~(k12\_borsuk\_1~X0~X1)~X0~(k11\_borsuk\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
(k12\_borsuk\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k11\_borsuk\_1~X0~X1))))))))\end{array}
\label{hyp:egehpflgbdcdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_eqrel\_1~X2~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
(k13\_borsuk\_1~X0~X1~X2=k2\_xboole\_0~X2~(ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X3 : \iota .  \preoh X3 \in u1\_struct\_0~\\
X1)~({\uniddcgcg} X3 : \iota .  k6\_domain\_1~(u1\_struct\_0~X0)~X3)))))\end{array}
\label{hyp:egjdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_eqrel\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(k12\_borsuk\_1~X0~X1=k13\_eqrel\_1~(u1\_struct\_0~X0)~X1))\end{array}
\label{hyp:egidpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfcgpgchdhfhlgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_eqrel\_1~X2~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((\preoh X3 \in u1\_struct\_0~\\
X1){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k11\_borsuk\_1~\\
X0~(k13\_borsuk\_1~X0~X1~X2)))~(k12\_borsuk\_1~X0~(k13\_borsuk\_1~X0~X1~\\
X2))~X3=k6\_domain\_1~(u1\_struct\_0~X0)~X3)))))\end{array}$$
\end{theorem}
\end{document}
