\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\_simplex0 (TMQuQunAiPwSckH6kk8QT6uRtdGFbawHQTk)}
\maketitle
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_simplex0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_simplex0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_setfam\_1 : {{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_matroid0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_simplex0}~{({{k1\_tarski}~{X0}})}}={{k9\_setfam\_1}~{X0}}}}\label{hyp:ehedpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(v1\_classes1~X1)){\unicdbdjdcd}(\\
r1\_tarski~(k1\_simplex0~X0)~X1)\end{array}
\label{hyp:ehddpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{({{k1\_tarski}~{X0}})}}~{X1}})}{\unicdbdjded}{({{X0} \in {X1}})}}}}\label{hyp:ehddbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(\preoh (v1\_finset\_1~(u1\_pre\_topc~X0)){\unicdcdcdhd}\\
((\preoh v2\_simplex0~X0){\unicdcdcdhd}(v3\_matroid0~X0)))\end{array}
\label{hyp:ehbdjdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_finset\_1}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v1\_finset\_1}~{({{k1\_zfmisc\_1}~{X0}})}}}})}}}\label{hyp:ggdgjdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}(v1\_classes1~\\
(k1\_matroid0~X0))\end{array}
\label{hyp:ggdgbdpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v3\_matroid0~X0){\unicdbdjded}(v5\_finset\_1~\\
(k1\_matroid0~X0)))\end{array}
\label{hyp:eggdpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v5\_finset\_1}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {{({{X1} \in {X0}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X1}})}}})}}}\label{hyp:eggdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{{k1\_matroid0}~{X0}}={{u1\_pre\_topc}~{X0}}})}}}\label{hyp:egbdpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_finset\_1~X1))\end{array}
\label{hyp:dgdgcdpfggjgogdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfdhjgngahmgfgihad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(((v1\_matroid0~X0){\unicdcdcdhd}(v1\_finset\_1~\\
(u1\_pre\_topc~X0))){\unicdbdjdcd}(v2\_simplex0~X0))\end{array}$$
\end{theorem}
\end{document}
