\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{l5\_topalg\_2 (TMTcUF7ughYim8VqmsjkEHJ62nXyAi5VkUN)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_borsuk\_1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
{{k5\_topmetr}={k17\_borsuk\_1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k17\_borsuk\_1){\unicdcdcdhd}((v1\_pre\_topc~k17\_borsuk\_1){\unicdcdcdhd}(\\
v2\_pre\_topc~k17\_borsuk\_1))\end{array}
\label{hyp:ggdgjdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v2\_pre\_topc}~{k3\_topmetr}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{k3\_topmetr}})}}\label{hyp:egehpflgddpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}((v1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_pre\_topc~(k2\_borsuk\_1~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgcdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{l1\_pre\_topc}~{k17\_borsuk\_1}}\label{hyp:egehpflgbdhdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_pre\_topc~\\
X2){\unicdcdcdhd}((v2\_pre\_topc~X2){\unicdcdcdhd}(l1\_pre\_topc~X2))){\unicdbdjdcd}((X2=k2\_borsuk\_1~\\
X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(u1\_pre\_topc~X2=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X2)))))~({\uniddcgcg} X3 : \iota .  \\
r1\_tarski~X3~(ReplSep2~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))~({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(u1\_struct\_0~X1))))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \\
(X4 \in u1\_pre\_topc~X0){\unicdcdcdhd}(X5 \in u1\_pre\_topc~X1))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \\
\iota .  k8\_mcart\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X4~X5)))~({\uniddcgcg} X3 : \\
\iota .  k5\_setfam\_1~(u1\_struct\_0~X2)~X3))))))\end{array}
\label{hyp:egcdpfcgpgchdhfhlgpfbd}
\end{equation}
\begin{theorem}\label{thm:mgfdpfehpgahbgmghgpfcd}
$$\begin{array}{c}u1\_struct\_0~(k2\_borsuk\_1~k3\_topmetr~k5\_topmetr)=k2\_zfmisc\_1~\\
(u1\_struct\_0~k3\_topmetr)~(u1\_struct\_0~k5\_topmetr)\end{array}$$
\end{theorem}
\end{document}
