\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\_3 (TMFyepSiqEPWtCNNrF8KLHuvfu6DSHABZLJ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compts\_1 : {{\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 $ m1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v1\_compts\_1~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~\\
X1){\unicdcdcdhd}((v1\_compts\_1~X1){\unicdcdcdhd}(l1\_pre\_topc~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~\\
X1~X0))))){\unicdbdjdcd}(((m1\_setfam\_1~X3~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0))){\unicdcdcdhd}\\
((v1\_tops\_2~X3~(k2\_borsuk\_1~X1~X0)){\unicdcdcdhd}(X2=ReplSep~(toset~({\uniddcgcg} X4 : \\
\iota .  (v3\_pre\_topc~X4~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))~({\uniddcgcg} X4 : \iota .  {\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0))))){\unicdcdcdhd}((r1\_tarski~\\
X5~X3){\unicdcdcdhd}((v1\_finset\_1~X5){\unicdcdcdhd}(r1\_tarski~(k3\_borsuk\_1~X1~X0~(k2\_struct\_0~\\
X1)~X4)~(k5\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0))~X5)))))~\\
({\uniddcgcg} X4 : \iota .  X4)))){\unicdbdjdcd}((v1\_tops\_2~X2~X0){\unicdcdcdhd}(m1\_setfam\_1~X2~(u1\_struct\_0~\\
X0)))))))\end{array}
\label{hyp:ehbdidpfcgpgchdhfhlgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_compts\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
(\preoh (m1\_setfam\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_tops\_2~X1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
(\preoh (r1\_tarski~X2~X1){\unicdcdcdhd}((m1\_setfam\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(v1\_finset\_1~\\
X2))))))))\end{array}
\label{hyp:egbdpfdgpgngahehdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfcgpgchdhfhlgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v1\_compts\_1~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~\\
X1){\unicdcdcdhd}((v1\_compts\_1~X1){\unicdcdcdhd}(l1\_pre\_topc~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~\\
X1~X0))))){\unicdbdjdcd}(\preoh (m1\_setfam\_1~X3~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0))){\unicdcdcdhd}\\
((v1\_tops\_2~X3~(k2\_borsuk\_1~X1~X0)){\unicdcdcdhd}((X2=ReplSep~(toset~({\uniddcgcg} X4 : \\
\iota .  (v3\_pre\_topc~X4~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))~({\uniddcgcg} X4 : \iota .  {\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0))))){\unicdcdcdhd}((r1\_tarski~\\
X5~X3){\unicdcdcdhd}((v1\_finset\_1~X5){\unicdcdcdhd}(r1\_tarski~(k3\_borsuk\_1~X1~X0~(k2\_struct\_0~\\
X1)~X4)~(k5\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0))~X5)))))~\\
({\uniddcgcg} X4 : \iota .  X4)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(\\
k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (r1\_tarski~X4~X2){\unicdcdcdhd}((v1\_finset\_1~\\
X4){\unicdcdcdhd}(m1\_setfam\_1~X4~(u1\_struct\_0~X0)))))))))))\end{array}$$
\end{theorem}
\end{document}
