\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{t7\_topalg\_6 (TMVt1niycMaAPHuAzCH7VzH97JVWryBuvvG)}
\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 $ 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 $ r1\_borsuk\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~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~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_borsuk\_2~X6~X0~X2~X3){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_borsuk\_2~X7~X0~X2~X3){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_borsuk\_2~X8~X1~X4~X5){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_borsuk\_2~\\
X9~X1~X4~X5){\unicdbdjdcd}(((r1\_borsuk\_6~X1~X4~X5){\unicdcdcdhd}((r1\_borsuk\_6~X0~X2~X3){\unicdcdcdhd}((\\
r1\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~X1)~X6~X8){\unicdcdcdhd}((r1\_funct\_2~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~X0)~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
X1)~X7~X9){\unicdcdcdhd}(r3\_borsuk\_2~X1~X4~X5~X8~X9))))){\unicdbdjdcd}(r3\_borsuk\_2~X0~X2~X3~\\
X6~X7)))))))))))\end{array}
\label{hyp:ehgdpfehpgahbgmghgpfgd}
\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 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_borsuk\_6~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_borsuk\_2~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_borsuk\_2~X4~X0~X1~X2){\unicdbdjdcd}\\
((k6\_eqrel\_1~(k1\_topalg\_1~X0~X1~X2)~(k1\_topalg\_1~X0~X1~X2)~(k3\_topalg\_1~\\
X0~X1~X2)~X3=k6\_eqrel\_1~(k1\_topalg\_1~X0~X1~X2)~(k1\_topalg\_1~X0~X1~\\
X2)~(k3\_topalg\_1~X0~X1~X2)~X4){\unicdbdjded}(r3\_borsuk\_2~X0~X1~X2~X3~X4)))))))\end{array}
\label{hyp:ehedgdpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(l1\_pre\_topc~X1))\end{array}
\label{hyp:egehpfngbdpfahchfgpfehpgahdg}
\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\_pre\_topc~X1~X0){\unicdbdjdcd}(v2\_pre\_topc~X1))\end{array}
\label{hyp:dgdgbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehhdpfehpgahbgmghgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_borsuk\_2~X6~X0~X2~X3){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_borsuk\_2~X7~X0~X2~X3){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_borsuk\_2~X8~X1~X4~X5){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_borsuk\_2~\\
X9~X1~X4~X5){\unicdbdjdcd}(((r1\_borsuk\_6~X1~X4~X5){\unicdcdcdhd}((r1\_borsuk\_6~X0~X2~X3){\unicdcdcdhd}((\\
r1\_funct\_2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~X1)~X6~X8){\unicdcdcdhd}((r1\_funct\_2~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~X0)~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
X1)~X7~X9){\unicdcdcdhd}(k6\_eqrel\_1~(k1\_topalg\_1~X1~X4~X5)~(k1\_topalg\_1~X1~X4~\\
X5)~(k3\_topalg\_1~X1~X4~X5)~X8=k6\_eqrel\_1~(k1\_topalg\_1~X1~X4~X5)~(\\
k1\_topalg\_1~X1~X4~X5)~(k3\_topalg\_1~X1~X4~X5)~X9))))){\unicdbdjdcd}(k6\_eqrel\_1~\\
(k1\_topalg\_1~X0~X2~X3)~(k1\_topalg\_1~X0~X2~X3)~(k3\_topalg\_1~X0~X2~X3)~\\
X6=k6\_eqrel\_1~(k1\_topalg\_1~X0~X2~X3)~(k1\_topalg\_1~X0~X2~X3)~(k3\_topalg\_1~\\
X0~X2~X3)~X7)))))))))))\end{array}$$
\end{theorem}
\end{document}
