\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{l48\_topalg\_1 (TMcVmxkUbiB2EDJBbLM4UL1HcQRDh8z89F4)}
\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_borsuk\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ r2\_borsuk\_2 : {{\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\_borsuk\_2~X3~\\
X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_borsuk\_2~X4~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_borsuk\_2~\\
X5~X0~X1~X2){\unicdbdjdcd}(((r3\_borsuk\_2~X0~X1~X2~X3~X4){\unicdcdcdhd}(r3\_borsuk\_2~X0~X1~X2~X4~\\
X5)){\unicdbdjdcd}(r3\_borsuk\_2~X0~X1~X2~X3~X5)))))))\end{array}
\label{hyp:ehhdjdpfcgpgchdhfhlgpfgd}
\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}({\unicdcdadad} X3 .  (m1\_borsuk\_2~X3~\\
X0~X1~X2){\unicdbdjdcd}((r2\_borsuk\_2~X0~X1~X2){\unicdbdjdcd}(r3\_borsuk\_2~X0~X1~X2~X3~X3)))))\end{array}
\label{hyp:ehbdcdpfcgpgchdhfhlgpfcd}
\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}(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}((r3\_borsuk\_2~X0~X1~X2~X3~X4){\unicdbdjdcd}(r3\_borsuk\_2~X0~X1~\\
X2~X4~X3))\end{array}
\label{hyp:dhjhngngfgehchjhpfchddpfcgpgchdhfhlgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  (({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjdcd}(X0~\\
X2~X2)){\unicdcdcdhd}(({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X0~X2~X3){\unicdbdjdcd}(X0~X3~X2)){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((X0~X2~X3){\unicdcdcdhd}(X0~X3~X4)){\unicdbdjdcd}(X0~X2~X4)))){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}((v1\_partfun1~X2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)))))){\unicdcdcdhd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
(k4\_tarski~X3~X4 \in X2){\unicdbdjded}((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}(X0~X3~X4)))))\end{array}
\label{hyp:dhbdpffgbhchfgmgpfbd}
\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}((r2\_borsuk\_2~X0~X1~X2){\unicdbdjded}(r1\_borsuk\_2~\\
X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfcgpgchdhfhlgpfcd}
\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 .  ((\preoh v2\_struct\_0~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 .  (X3=k1\_topalg\_1~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  \\
(X4 \in X3){\unicdbdjded}(m1\_borsuk\_2~X4~X0~X1~X2)))))\end{array}
\label{hyp:egbdpfehpgahbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:mgedidpfehpgahbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (r1\_borsuk\_6~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
((v1\_partfun1~X3~(k1\_topalg\_1~X0~X1~X2)){\unicdcdcdhd}((v3\_relat\_2~X3){\unicdcdcdhd}((v8\_relat\_2~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_topalg\_1~X0~\\
X1~X2)~(k1\_topalg\_1~X0~X1~X2))))))){\unicdbdjdcd}(\preoh {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (k4\_tarski~\\
X4~X5 \in X3){\unicdbdjded}((X4 \in k1\_topalg\_1~X0~X1~X2){\unicdcdcdhd}((X5 \in k1\_topalg\_1~X0~X1~X2){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m1\_borsuk\_2~X6~X0~X1~X2){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_borsuk\_2~\\
X7~X0~X1~X2){\unicdcdcdhd}((X6=X4){\unicdcdcdhd}((X7=X5){\unicdcdcdhd}(r3\_borsuk\_2~X0~X1~X2~X6~X7))))))))))))\end{array}$$
\end{theorem}
\end{document}
