\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{t9\_simplex2 (TMNzmGDnLbRJ6bYHyKcSX1i1DQzLKvtKf6U)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matroid0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_simplex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_simplex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m2\_simplex0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v6\_metric\_1~X1){\unicdcdcdhd}\\
(l1\_metric\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_simplex2~X2~X1){\unicdcdcdhd}(m1\_simplex0~\\
X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_simplex0~X3~X0~X2){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_simplex2~\\
X1~X3)~(k1\_simplex2~X1~X2))))\end{array}
\label{hyp:ehidpfdhjgngahmgfgihcd}
\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}(v1\_int\_1~X2)){\unicdbdjdcd}(m2\_simplex0~(k9\_simplex0~X0~X1~X2)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfdhjgngahmgfgihad}
\end{equation}
\begin{theorem}\label{thm:ehjdpfdhjgngahmgfgihcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v6\_metric\_1~X1){\unicdcdcdhd}\\
(l1\_metric\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matroid0~X2){\unicdcdcdhd}((v1\_simplex2~\\
X2~X1){\unicdcdcdhd}(m1\_simplex0~X2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k1\_simplex2~X1~(k9\_simplex0~X0~X2~X3))~(k1\_simplex2~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
