\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{t76\_borsuk\_5 (TMKBhSMeY2Sj93dcZYCteFubPkt513FDFXd)}
\maketitle
Let $ v2\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
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 $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (\preoh X1 \in X0){\unicdcdcdhd}(({\unicdcdaddd} X2 .  (v1\_xreal\_0~\\
X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (v1\_xreal\_0~X3){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
X1~X2){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X3~X1)))))){\unicdcdcdhd}(v2\_connsp\_1~X0~k3\_topmetr))))\end{array}
\label{hyp:ehddpfehpgahchfgbgmgfd}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k3\_topmetr}}={k1\_numbers}}\label{hyp:ehbdhdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:mgbdpfchfgbgmg}
\end{equation}
\begin{theorem}\label{thm:ehhdgdpfcgpgchdhfhlgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_connsp\_1~X0~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(u1\_struct\_0~k3\_topmetr)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X1~X2){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}((X1 \in X0){\unicdcdcdhd}(X3 \in X0)))){\unicdbdjdcd}(X2 \in X0)))))\end{array}$$
\end{theorem}
\end{document}
