\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{l36\_metrizts (TMQVQJJpZTD2QxtFWCLYGdybY8e62Uaoigz)}
\maketitle
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pcomps\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_metrizts : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_topgen\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_waybel23 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_topgen\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_waybel23 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_finset\_1~X1){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}((r1\_ordinal1~\\
(k2\_waybel23~X0)~X1){\unicdbdjded}(r1\_ordinal1~(k4\_topgen\_1~X0)~X1)))\end{array}
\label{hyp:ehcdcdpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v1\_metrizts~X0){\unicdbdjded}(v5\_waybel23~X0))\end{array}
\label{hyp:mgddfdpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_finset\_1}~{k4\_ordinal1}}}}\label{hyp:ggdghdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_card\_1}~{k4\_ordinal1}}\label{hyp:ggdgedpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v5\_waybel23~X0){\unicdbdjded}(r1\_ordinal1~\\
(k2\_waybel23~X0)~k4\_ordinal1))\end{array}
\label{hyp:eggdpfhhbgjhcgfgmgcddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}((v7\_topgen\_1~\\
X0){\unicdbdjded}(r1\_ordinal1~(k4\_topgen\_1~X0)~k4\_ordinal1))\end{array}
\label{hyp:egbdddpfehpgahhgfgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~\\
X0){\unicdcdcdhd}(v1\_metrizts~X0))){\unicdbdjdcd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v5\_waybel23~X0){\unicdcdcdhd}\\
(v3\_pcomps\_1~X0))))\end{array}
\label{hyp:dgdgfdpfngfgehchjgkhehdh}
\end{equation}
\begin{theorem}\label{thm:mgddgdpfngfgehchjgkhehdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v1\_metrizts~X0){\unicdbdjded}(v7\_topgen\_1~X0))\end{array}$$
\end{theorem}
\end{document}
