\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}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t56\_glib\_003 (TMKpLkBYwXSAsVMHtjyhyFm5yKYUtFBSPkC)}
\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 $ v2\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_glib\_003 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_glib\_003 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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){\unicdcdcdhd}((v2\_glib\_003~X0){\unicdcdcdhd}\\
(v3\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k7\_glib\_003~X0=\\
k7\_glib\_003~(k12\_glib\_003~X0~X1~X2))\end{array}
\label{hyp:ehddgdpfhgmgjgcgpfadaddd}
\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}((v2\_glib\_003~X0){\unicdcdcdhd}(v3\_glib\_003~X0))))))){\unicdbdjdcd}((v1\_relat\_1~\\
(k12\_glib\_003~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k12\_glib\_003~X0~X1~X2)~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~(k12\_glib\_003~X0~X1~X2)){\unicdcdcdhd}((v1\_finset\_1~(k12\_glib\_003~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_glib\_000~(k12\_glib\_003~X0~X1~X2)){\unicdcdcdhd}((v2\_glib\_003~\\
(k12\_glib\_003~X0~X1~X2)){\unicdcdcdhd}(v3\_glib\_003~(k12\_glib\_003~X0~X1~X2))))))))\end{array}
\label{hyp:ggdghdedpfhgmgjgcgpfadaddd}
\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\_003~X0)))))){\unicdbdjdcd}\\
(k14\_glib\_003~X0=k9\_xtuple\_0~(k7\_glib\_003~X0))\end{array}
\label{hyp:egcdddpfhgmgjgcgpfadaddd}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfhgmgjgcgpfadaddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v2\_glib\_003~X0){\unicdcdcdhd}\\
(v3\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k14\_glib\_003~\\
X0=k14\_glib\_003~(k12\_glib\_003~X0~X1~X2))\end{array}$$
\end{theorem}
\end{document}
