\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{t41\_borsuk\_5 (TMLovn2xwgDrcavZe1qWqeREDKFnAKmYMfz)}
\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 $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}((X0=\\
X1){\unicdbdjdcd}((v2\_rcomp\_1~X0){\unicdbdjded}(v4\_pre\_topc~X1~k3\_topmetr))))\end{array}
\label{hyp:ehcdddpfkgpgchegbgogfdbg}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k3\_topmetr}}={k1\_numbers}}\label{hyp:ehbdhdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v2\_rcomp\_1}~{({{{k4\_rcomp\_1}~{k2\_xxreal\_0}}~{X0}})}})}}}\label{hyp:mgedgdpfcgpgchdhfhlgpffd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfcgpgchdhfhlgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topmetr))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((X0=k4\_rcomp\_1~k2\_xxreal\_0~X1){\unicdbdjdcd}\\
(v4\_pre\_topc~X0~k3\_topmetr)))\end{array}$$
\end{theorem}
\end{document}
