\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{t20\_metrizts (TMUTwimq1ymcP6p74wXiehfW9jAqs58xDKC)}
\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\_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 $ 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 $ v2\_tex\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v4\_pre\_topc~X2~X0){\unicdcdcdhd}(v2\_tex\_2~X2~X0)){\unicdbdjdcd}(\\
r1\_ordinal1~(k1\_card\_1~X2)~X1)))))\end{array}
\label{hyp:ehbdjdpfngfgehchjgkhehdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_finset\_1~X0){\unicdcdcdhd}(v1\_card\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
(v2\_pre\_topc~X1){\unicdcdcdhd}((v3\_pcomps\_1~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}(((v4\_pre\_topc~\\
X2~X1){\unicdcdcdhd}(v2\_tex\_2~X2~X1)){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~X2)~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}((v2\_tex\_2~X2~\\
X1){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~X2)~X0)))))\end{array}
\label{hyp:ehbdedpfngfgehchjgkhehdh}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfngfgehchjgkhehdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v3\_pcomps\_1~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_finset\_1~X1){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}((r1\_ordinal1~\\
(k2\_waybel23~X0)~X1){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((v2\_tex\_2~X2~X0){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~\\
X2)~X1)))))\end{array}$$
\end{theorem}
\end{document}
