\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{t40\_matroid0 (TMb9VxNst1FUSxVdPtoKBTwSQgB7TeD684v)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\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\_matroid0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_matroid0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_matroid0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_matroid0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v3\_pencil\_1~X0){\unicdcdcdhd}((v1\_matroid0~\\
X0){\unicdcdcdhd}((v2\_matroid0~X0){\unicdcdcdhd}((v4\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((v5\_matroid0~X1~X0){\unicdbdjded}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2 \in X1){\unicdbdjdcd}(r1\_matroid0~X0~(k7\_subset\_1~(\\
u1\_struct\_0~X0)~X1~(k6\_domain\_1~(u1\_struct\_0~X0)~X2))~X1))))))\end{array}
\label{hyp:ehddidpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v3\_pencil\_1~X0){\unicdcdcdhd}((v1\_matroid0~\\
X0){\unicdcdcdhd}((v2\_matroid0~X0){\unicdcdcdhd}((v4\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
u1\_struct\_0~X0)))){\unicdbdjdcd}((v3\_pre\_topc~X1~X0){\unicdbdjded}(k5\_card\_1~X1=k4\_matroid0~\\
X0~X1)))\end{array}
\label{hyp:ehcdbdpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v3\_pencil\_1~X0){\unicdcdcdhd}((v1\_matroid0~\\
X0){\unicdcdcdhd}((v2\_matroid0~X0){\unicdcdcdhd}((v4\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v3\_pre\_topc~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}((r1\_matroid0~X0~X2~X1){\unicdbdjded}((r1\_tarski~X2~X1){\unicdcdcdhd}\\
(k5\_card\_1~X2=k4\_matroid0~X0~X1)))))\end{array}
\label{hyp:ehbdjdpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X0 \in X1){\unicdbdjdcd}(k2\_xboole\_0~(k4\_xboole\_0~X1~(\\
k1\_tarski~X0))~(k1\_tarski~X0)=X1)\end{array}
\label{hyp:ehbdbdgdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_finset\_1~X0){\unicdbdjdcd}(v1\_finset\_1~(k4\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ggdgbdcdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(m1\_subset\_1~(k7\_subset\_1~X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflghdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k6\_domain\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((v5\_matroid0~X1~X0){\unicdbdjded}((\preoh v3\_pre\_topc~X1~X0){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2 \in X1){\unicdbdjdcd}(v3\_pre\_topc~\\
(k7\_subset\_1~(u1\_struct\_0~X0)~X1~(k1\_tarski~X2))~X0))))))\end{array}
\label{hyp:egbdgdpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v3\_pencil\_1~X0){\unicdcdcdhd}((v1\_matroid0~\\
X0){\unicdcdcdhd}((v2\_matroid0~X0){\unicdcdcdhd}((v4\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((r2\_matroid0~X0~X1~X2){\unicdbdjded}(k4\_matroid0~\\
X0~(k4\_subset\_1~(u1\_struct\_0~X0)~X2~(k6\_domain\_1~(u1\_struct\_0~\\
X0)~X1))=k4\_matroid0~X0~X2))))\end{array}
\label{hyp:egbdedpfngbgehchpgjgegad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v3\_pencil\_1~X0){\unicdcdcdhd}((v1\_matroid0~\\
X0){\unicdcdcdhd}((v2\_matroid0~X0){\unicdcdcdhd}((v4\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((v5\_matroid0~X1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))\end{array}
\label{hyp:dgdghdpfngbgehchpgjgegad}
\end{equation}
\begin{theorem}\label{thm:ehedadpfngbgehchpgjgegad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v3\_pencil\_1~X0){\unicdcdcdhd}((v1\_matroid0~\\
X0){\unicdcdcdhd}((v2\_matroid0~X0){\unicdcdcdhd}((v4\_matroid0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(((v5\_matroid0~\\
X1~X0){\unicdcdcdhd}(X2 \in X1)){\unicdbdjdcd}(r2\_matroid0~X0~X2~(k7\_subset\_1~(u1\_struct\_0~\\
X0)~X1~(k6\_domain\_1~(u1\_struct\_0~X0)~X2))))))\end{array}$$
\end{theorem}
\end{document}
