\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{t29\_simplex0 (TMLNQeMysp56NhpHv3LQFoB3D8wdCZQFmvx)}
\maketitle
Let $ v1\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_simplex0 : {{\iota}{\unicdbdjdcd}{{\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 $ v5\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_simplex0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_matroid0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_simplex0~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v5\_finset\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X2)))){\unicdbdjdcd}((r1\_tarski~\\
(k2\_simplex0~X2~X3)~(u1\_pre\_topc~X1)){\unicdbdjdcd}((v1\_pre\_topc~(k5\_simplex0~\\
X2~X3)){\unicdcdcdhd}(m2\_simplex0~(k5\_simplex0~X2~X3)~X0~X1)))))\end{array}
\label{hyp:ehcdidpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(k2\_simplex0~X0~X1=k1\_simplex0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdhjgngahmgfgihad}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m1\_simplex0}~{X1}}~{X0}})}{\unicdbdjdcd}{({{l1\_pre\_topc}~{X1}})}}}}\label{hyp:egehpfngbdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}((v1\_pre\_topc~(k5\_simplex0~X0~X1)){\unicdcdcdhd}(m1\_simplex0~(k5\_simplex0~\\
X0~X1)~X0))\end{array}
\label{hyp:egehpflgfdpfdhjgngahmgfgihad}
\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}
\begin{theorem}\label{thm:ehcdjdpfdhjgngahmgfgihad}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_matroid0~X1){\unicdcdcdhd}(m1\_simplex0~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v5\_finset\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k1\_zfmisc\_1~X2)))){\unicdbdjdcd}((r1\_tarski~X3~(u1\_pre\_topc~X1)){\unicdbdjdcd}((v1\_pre\_topc~\\
(k5\_simplex0~X2~X3)){\unicdcdcdhd}(m2\_simplex0~(k5\_simplex0~X2~X3)~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
