\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{t36\_topalg\_1 (TMMWhazKE7HowjhpssHVkfmBSsCbhno1Nm7)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_borsuk\_2 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r4\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ r1\_borsuk\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r1\_borsuk\_6~\\
X0~X1~X2){\unicdcdcdhd}((r1\_borsuk\_6~X0~X2~X3){\unicdcdcdhd}((r1\_borsuk\_6~X0~X3~X4){\unicdcdcdhd}(r1\_borsuk\_6~\\
X0~X4~X5)))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_borsuk\_2~X6~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_borsuk\_2~X7~X0~X2~X3){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_borsuk\_2~X8~X0~X3~X4){\unicdbdjdcd}\\
({\unicdcdadad} X9 .  (m1\_borsuk\_2~X9~X0~X4~X5){\unicdbdjdcd}(r3\_borsuk\_2~X0~X1~X5~(k1\_borsuk\_2~\\
X0~X1~X4~X5~(k1\_borsuk\_2~X0~X1~X2~X4~X6~(k1\_borsuk\_2~X0~X2~X3~X4~X7~X8))~\\
X9)~(k1\_borsuk\_2~X0~X1~X3~X5~(k1\_borsuk\_2~X0~X1~X2~X3~X6~X7)~(k1\_borsuk\_2~\\
X0~X3~X4~X5~X8~X9)))))))))))))\end{array}
\label{hyp:ehddfdpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v1\_borsuk\_2~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((m1\_borsuk\_2~X3~X0~X1~X2){\unicdcdcdhd}(m1\_borsuk\_2~X4~X0~X1~X2))))){\unicdbdjdcd}(\\
(r4\_borsuk\_2~X0~X1~X2~X3~X4){\unicdbdjded}(r3\_borsuk\_2~X0~X1~X2~X3~X4))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchedpfcgpgchdhfhlgpfcd}
\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}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}((r1\_borsuk\_6~X0~X1~X2){\unicdbdjded}(r1\_borsuk\_2~\\
X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}(\\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_borsuk\_2~X4~X0~X1~\\
X2){\unicdcdcdhd}(m1\_borsuk\_2~X5~X0~X2~X3)))))){\unicdbdjdcd}(m1\_borsuk\_2~(k1\_borsuk\_2~\\
X0~X1~X2~X3~X4~X5)~X0~X1~X3)\end{array}
\label{hyp:egehpflgbdpfcgpgchdhfhlgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_borsuk\_2~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_borsuk\_2~X0~X1~X2))))\end{array}
\label{hyp:egddpfcgpgchdhfhlgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfehpgahbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v1\_borsuk\_2~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_borsuk\_2~X6~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_borsuk\_2~\\
X7~X0~X2~X3){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_borsuk\_2~X8~X0~X3~X4){\unicdbdjdcd}({\unicdcdadad} X9 .  (\\
m1\_borsuk\_2~X9~X0~X4~X5){\unicdbdjdcd}(r4\_borsuk\_2~X0~X1~X5~(k1\_borsuk\_2~X0~X1~\\
X4~X5~(k1\_borsuk\_2~X0~X1~X2~X4~X6~(k1\_borsuk\_2~X0~X2~X3~X4~X7~X8))~X9)~\\
(k1\_borsuk\_2~X0~X1~X3~X5~(k1\_borsuk\_2~X0~X1~X2~X3~X6~X7)~(k1\_borsuk\_2~\\
X0~X3~X4~X5~X8~X9))))))))))))\end{array}$$
\end{theorem}
\end{document}
