\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{t38\_simplex0 (TMameKbmmSFRjDKhwGCWGM7mgrarwpfhcKy)}
\maketitle
Let $ v1\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_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 $ k7\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m2\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v7\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_simplex0~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_simplex0~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_simplex0~X3~X0~X2){\unicdbdjdcd}(((v7\_simplex0~X2~\\
X0~X1){\unicdcdcdhd}(v7\_simplex0~X3~X0~X2)){\unicdbdjdcd}((v7\_simplex0~X3~X0~X1){\unicdcdcdhd}(m2\_simplex0~\\
X3~X0~X1)))))\end{array}
\label{hyp:ehddedpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_simplex0~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_simplex0~\\
X2~X0~X1){\unicdbdjdcd}((v1\_matroid0~X2){\unicdcdcdhd}((v3\_matroid0~X2){\unicdcdcdhd}(m1\_simplex0~X2~\\
X0))))\end{array}
\label{hyp:egehpfngcdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_matroid0~X1){\unicdcdcdhd}(m1\_simplex0~\\
X1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1)))){\unicdbdjdcd}((v1\_pre\_topc~\\
(k7\_simplex0~X0~X1~X2)){\unicdcdcdhd}((v7\_simplex0~(k7\_simplex0~X0~X1~X2)~X0~\\
X1){\unicdcdcdhd}(m2\_simplex0~(k7\_simplex0~X0~X1~X2)~X0~X1)))\end{array}
\label{hyp:egehpflghdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_matroid0~X1){\unicdcdcdhd}((v3\_matroid0~X1){\unicdcdcdhd}(\\
m1\_simplex0~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_pre\_topc~X3){\unicdcdcdhd}((v7\_simplex0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_simplex0~X3~X0~X1))){\unicdbdjdcd}((X3=k7\_simplex0~X0~X1~X2){\unicdbdjded}(\\
k2\_struct\_0~X3=X2))))\end{array}
\label{hyp:egbdgdpfdhjgngahmgfgihad}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdhjgngahmgfgihad}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_matroid0~X1){\unicdcdcdhd}((v3\_matroid0~X1){\unicdcdcdhd}(\\
m1\_simplex0~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k7\_simplex0~X0~X1~X2)))){\unicdbdjdcd}((X4=X3){\unicdbdjdcd}(k7\_simplex0~\\
X0~(k7\_simplex0~X0~X1~X2)~X4=k7\_simplex0~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
