\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{t13\_borsuk\_5 (TMdJsQzYNw67yHtnK1ejHY1A3YU66bd8Z5Y)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k8\_metric\_1 : {\iota}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_pcomps\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v7\_metric\_1~\\
X0){\unicdcdcdhd}((v8\_metric\_1~X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_pcomps\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2 \in k2\_pre\_topc~\\
(k3\_pcomps\_1~X0)~X1){\unicdbdjded}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X3~k6\_numbers){\unicdcdcdhd}(r1\_xboole\_0~(k9\_metric\_1~X0~X2~X3)~X1))))))\end{array}
\label{hyp:ehjdcdpfhgpgcgpgbgcheggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_metric\_1~k8\_metric\_1){\unicdcdcdhd}((v6\_metric\_1~k8\_metric\_1){\unicdcdcdhd}((v7\_metric\_1~\\
k8\_metric\_1){\unicdcdcdhd}((v8\_metric\_1~k8\_metric\_1){\unicdcdcdhd}(v9\_metric\_1~k8\_metric\_1))))\end{array}
\label{hyp:ggdggdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k8\_metric\_1}}}})}{\unicdcdcdhd}{({{v1\_metric\_1}~{k8\_metric\_1}})}}\label{hyp:ggdgfdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_metric\_1}~{k8\_metric\_1}})}{\unicdcdcdhd}{({{l1\_metric\_1}~{k8\_metric\_1}})}}\label{hyp:egehpflgidpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_topmetr}={{k3\_pcomps\_1}~{k8\_metric\_1}}}\label{hyp:eggdpfehpgahngfgehch}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfcgpgchdhfhlgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~k8\_metric\_1)){\unicdbdjdcd}((X1 \in \\
k2\_pre\_topc~k3\_topmetr~X0){\unicdbdjded}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh \\
r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}(r1\_xboole\_0~(k9\_metric\_1~k8\_metric\_1~\\
X1~X2)~X0)))))\end{array}$$
\end{theorem}
\end{document}
