\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{t19\_borsuk\_1 (TMZoAGPRcaWPUFAsALszb9GfLz2Y3jPwVMQ)}
\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\_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 $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k2\_borsuk\_1~X0~X1)))){\unicdbdjdcd}((v3\_pre\_topc~X2~(k2\_borsuk\_1~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
(((X3=k7\_relset\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))~(u1\_struct\_0~X0)~(k9\_funct\_3~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))~X2){\unicdbdjdcd}(v3\_pre\_topc~X3~X0)){\unicdcdcdhd}((X4=k7\_relset\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~X1)~(k10\_funct\_3~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~X2){\unicdbdjdcd}(v3\_pre\_topc~X4~X1))))))))\end{array}
\label{hyp:ehbdidpfcgpgchdhfhlgpfbd}
\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}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \preoh (X3 \in k7\_relset\_1~\\
(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~\\
(u1\_struct\_0~X1))~(k9\_borsuk\_1~X0~X1)~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))){\unicdbdjdcd}(\preoh (X4 \in X2){\unicdcdcdhd}\\
(X3=k7\_relset\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~\\
(u1\_struct\_0~X1)~(k10\_funct\_3~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~\\
X4))))))\end{array}
\label{hyp:ehbdhdpfcgpgchdhfhlgpfbd}
\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}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \preoh (X3 \in k7\_relset\_1~\\
(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~\\
(u1\_struct\_0~X0))~(k8\_borsuk\_1~X0~X1)~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))){\unicdbdjdcd}(\preoh (X4 \in X2){\unicdcdcdhd}\\
(X3=k7\_relset\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~\\
(u1\_struct\_0~X0)~(k9\_funct\_3~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~\\
X4))))))\end{array}
\label{hyp:ehbdgdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)\end{array}
\label{hyp:chdgcdpfdhfhcgdhfgehpfbd}
\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 v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)))){\unicdbdjdcd}((v1\_funct\_1~(k9\_borsuk\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k9\_borsuk\_1~\\
X0~X1)~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~\\
(u1\_struct\_0~X1))){\unicdcdcdhd}(m1\_subset\_1~(k9\_borsuk\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~\\
(k9\_setfam\_1~(u1\_struct\_0~X1)))))))\end{array}
\label{hyp:egehpflgjdpfcgpgchdhfhlgpfbd}
\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 v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)))){\unicdbdjdcd}((v1\_funct\_1~(k8\_borsuk\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_borsuk\_1~\\
X0~X1)~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~(k8\_borsuk\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~\\
(k9\_setfam\_1~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgidpfcgpgchdhfhlgpfbd}
\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~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(m1\_subset\_1~(k7\_relset\_1~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~X1))\end{array}
\label{hyp:egehpflghdpfchfgmgdhfgehpfbd}
\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 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((v1\_tops\_2~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((X2 \in X1){\unicdbdjdcd}(v3\_pre\_topc~\\
X2~X0)))))\end{array}
\label{hyp:egbdpfehpgahdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfcgpgchdhfhlgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~X0~X1))))){\unicdbdjdcd}((v1\_tops\_2~X2~(k2\_borsuk\_1~\\
X0~X1)){\unicdbdjdcd}((v1\_tops\_2~(k7\_relset\_1~(k9\_setfam\_1~(u1\_struct\_0~(\\
k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~(u1\_struct\_0~X0))~(k8\_borsuk\_1~\\
X0~X1)~X2)~X0){\unicdcdcdhd}(v1\_tops\_2~(k7\_relset\_1~(k9\_setfam\_1~(u1\_struct\_0~\\
(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~(u1\_struct\_0~X1))~(k9\_borsuk\_1~\\
X0~X1)~X2)~X1)))))\end{array}$$
\end{theorem}
\end{document}
