\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\_compl\_sp (TMUMdGk5x4PCn3xe5CNhrM5xQZy7ELNckcD)}
\maketitle
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compts\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_compl\_sp : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_card\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v8\_compl\_sp~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
(\preoh (m1\_setfam\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_tops\_2~X1~X0){\unicdcdcdhd}((v4\_card\_3~\\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(\preoh (r1\_tarski~X2~X1){\unicdcdcdhd}((m1\_setfam\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(v1\_finset\_1~X2)))))))))\end{array}
\label{hyp:egjdpfdgpgngahmgpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_compts\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
(\preoh (m1\_setfam\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_tops\_2~X1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
(\preoh (r1\_tarski~X2~X1){\unicdcdcdhd}((m1\_setfam\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(v1\_finset\_1~\\
X2))))))))\end{array}
\label{hyp:egbdpfdgpgngahehdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfdgpgngahmgpfdhah}
${{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{({{v1\_compts\_1}~{X0}})}{\unicdbdjdcd}{({{v8\_compl\_sp}~{X0}})}})}}}$.
\end{theorem}
\end{document}
