\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{t51\_helly (TMTvfqUbZN9fLXv62zUjUboNfzZ3KFMbLzc)}
\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 $ v5\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_helly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_helly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_helly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~(k1\_tarski~X0)~(k1\_tarski~X1)){\unicdbdjdcd}\\
(X0=X1)\end{array}
\label{hyp:ehddpfkhggngjgdhdgpfbd}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k6\_glib\_000~\\
X0)){\unicdbdjdcd}((X3 \in k13\_glib\_001~X0~(k2\_helly~X0~X1~X2)){\unicdbdjded}(r1\_tarski~(k2\_helly~\\
X0~X1~X3)~(k2\_helly~X0~X1~X2))))))\end{array}
\label{hyp:ehddhdpfigfgmgmgjh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k6\_glib\_000~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v5\_glib\_001~X4~X0){\unicdcdcdhd}(m3\_glib\_001~X4~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X5 .  ((v5\_glib\_001~X5~X0){\unicdcdcdhd}(m3\_glib\_001~X5~X0)){\unicdbdjdcd}(((X4=k2\_helly~\\
X0~X1~X2){\unicdcdcdhd}(X5=k2\_helly~X0~X1~X3)){\unicdbdjdcd}((r1\_tarski~X4~X5){\unicdcdcdid}((r1\_tarski~\\
X5~X4){\unicdcdcdid}(k9\_subset\_1~(k6\_glib\_000~X0)~(k9\_subset\_1~(k6\_glib\_000~\\
X0)~(k13\_glib\_001~X0~X4)~(k13\_glib\_001~X0~(k2\_helly~X0~X2~X3)))~(\\
k13\_glib\_001~X0~(k2\_helly~X0~X3~X1))=k1\_tarski~(k1\_funct\_1~X4~(\\
k3\_finseq\_1~(k1\_helly~X4~X5))))))))))))\end{array}
\label{hyp:mgededpfigfgmgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((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)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k6\_glib\_000~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k3\_helly~X0~X1~X2~X3)~(k6\_glib\_000~\\
X0))\end{array}
\label{hyp:egehpflgddpfigfgmgmgjh}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k6\_glib\_000~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k6\_glib\_000~X0)){\unicdbdjdcd}((X4=k3\_helly~\\
X0~X1~X2~X3){\unicdbdjded}(k9\_subset\_1~(k6\_glib\_000~X0)~(k9\_subset\_1~(k6\_glib\_000~\\
X0)~(k13\_glib\_001~X0~(k2\_helly~X0~X1~X2))~(k13\_glib\_001~X0~(k2\_helly~\\
X0~X2~X3)))~(k13\_glib\_001~X0~(k2\_helly~X0~X3~X1))=k1\_tarski~X4))))))\end{array}
\label{hyp:egddpfigfgmgmgjh}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfigfgmgmgjh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v3\_glib\_002~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v5\_glib\_001~X1~X0){\unicdcdcdhd}(m3\_glib\_001~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v5\_glib\_001~X2~X0){\unicdcdcdhd}(m3\_glib\_001~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k6\_glib\_000~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k6\_glib\_000~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k6\_glib\_000~X0)){\unicdbdjdcd}(((X1=k2\_helly~\\
X0~X3~X4){\unicdcdcdhd}(X2=k2\_helly~X0~X3~X5)){\unicdbdjdcd}((X4 \in k13\_glib\_001~X0~X2){\unicdcdcdid}((X5 \in \\
k13\_glib\_001~X0~X1){\unicdcdcdid}(k3\_helly~X0~X3~X4~X5=k1\_funct\_1~X1~(k3\_finseq\_1~\\
(k1\_helly~X1~X2)))))))))))\end{array}$$
\end{theorem}
\end{document}
