\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\_helly (TMN8xTcSc5sPvnmFp4Be1W4Pq5XeUaYup3Z)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_glib\_002 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_helly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}((k3\_glib\_001~X0~X1 \in k13\_glib\_001~X0~X1){\unicdcdcdhd}(k4\_glib\_001~X0~\\
X1 \in k13\_glib\_001~X0~X1)))\end{array}
\label{hyp:ehididpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v3\_glib\_002~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k6\_glib\_000~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k6\_glib\_000~X0)){\unicdbdjdcd}((k3\_glib\_001~X0~(k2\_helly~X0~X1~X2)=X1){\unicdcdcdhd}\\
(k4\_glib\_001~X0~(k2\_helly~X0~X1~X2)=X2))))\end{array}
\label{hyp:ehcdidpfigfgmgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~\\
X0){\unicdcdcdhd}(v3\_glib\_002~X0)))))){\unicdcdcdhd}((m1\_subset\_1~X1~(k6\_glib\_000~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k6\_glib\_000~X0)))){\unicdbdjdcd}((v5\_glib\_001~(k2\_helly~\\
X0~X1~X2)~X0){\unicdcdcdhd}(m3\_glib\_001~(k2\_helly~X0~X1~X2)~X0))\end{array}
\label{hyp:egehpflgcdpfigfgmgmgjh}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfigfgmgmgjh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v3\_glib\_002~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k6\_glib\_000~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k6\_glib\_000~X0)){\unicdbdjdcd}((X1 \in k13\_glib\_001~X0~(k2\_helly~X0~X1~X2)){\unicdcdcdhd}\\
(X2 \in k13\_glib\_001~X0~(k2\_helly~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
