\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{t45\_topalg\_1 (TMT47GsteUmK75bLvPsLUbgpgZEGvqdo1Fd)}
\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 $ m1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ 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.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v3\_relat\_2~X3){\unicdcdcdhd}\\
((v1\_partfun1~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))))){\unicdbdjdcd}((X1 \in k6\_eqrel\_1~X0~X0~X3~X2){\unicdbdjded}(k4\_tarski~X1~X2 \in X3))\end{array}
\label{hyp:ehbdjdpffgbhchfgmgpfbd}
\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 .  ((\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}((\preoh \\
v1\_xboole\_0~(k3\_topalg\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k3\_topalg\_1~\\
X0~X1~X2)~(k1\_topalg\_1~X0~X1~X2)){\unicdcdcdhd}((v3\_relat\_2~(k3\_topalg\_1~X0~X1~\\
X2)){\unicdcdcdhd}(v8\_relat\_2~(k3\_topalg\_1~X0~X1~X2))))))))\end{array}
\label{hyp:mgfdadpfehpgahbgmghgpfbd}
\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}(m1\_subset\_1~(k3\_topalg\_1~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_topalg\_1~X0~X1~X2)~(k1\_topalg\_1~\\
X0~X1~X2))))\end{array}
\label{hyp:egehpflgddpfehpgahbgmghgpfbd}
\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\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_topalg\_1~X0~X1~X2)~\\
(k1\_topalg\_1~X0~X1~X2)))){\unicdbdjdcd}((X3=k3\_topalg\_1~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  \\
(m1\_borsuk\_2~X4~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_borsuk\_2~X5~X0~X1~X2){\unicdbdjdcd}\\
((k4\_tarski~X4~X5 \in X3){\unicdbdjded}(r3\_borsuk\_2~X0~X1~X2~X4~X5)))))))))\end{array}
\label{hyp:egddpfehpgahbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfehpgahbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_borsuk\_6~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_borsuk\_2~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_borsuk\_2~X4~X0~X1~X2){\unicdbdjdcd}\\
((X4 \in k6\_eqrel\_1~(k1\_topalg\_1~X0~X1~X2)~(k1\_topalg\_1~X0~X1~X2)~(k3\_topalg\_1~\\
X0~X1~X2)~X3){\unicdbdjded}(r3\_borsuk\_2~X0~X1~X2~X3~X4)))))))\end{array}$$
\end{theorem}
\end{document}
