\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{l50\_topalg\_1 (TMHRsn8tKk4gMtD8yQ7NWXRPyBAYzgmn94U)}
\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\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\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}(\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}
\label{hyp:mgedidpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~\\
X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}((k4\_tarski~X3~X1 \in X2){\unicdbdjded}(k6\_eqrel\_1~\\
X0~X0~X2~X3=k6\_eqrel\_1~X0~X0~X2~X1)))\end{array}
\label{hyp:mgcdgdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\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)))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_topalg\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgbdpfehpgahbgmghgpfbd}
\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}
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:mgfdadpfehpgahbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_borsuk\_6~X0~X1~X2){\unicdbdjdcd}((\preoh \\
v1\_xboole\_0~(k3\_topalg\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k3\_topalg\_1~\\
X0~X1~X2)~(k1\_topalg\_1~X0~X1~X2)){\unicdcdcdhd}((v3\_relat\_2~(k3\_topalg\_1~X0~X1~\\
X2)){\unicdcdcdhd}(v8\_relat\_2~(k3\_topalg\_1~X0~X1~X2))))))))\end{array}$$
\end{theorem}
\end{document}
