\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=}
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\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\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{t30\_glib\_003 (TMbtErKTmrGbpj4k3BcW5kt4QUStKQuDWCH)}
\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 $ v1\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m4\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((X2 \in k4\_finseq\_1~X0){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(\\
k1\_seq\_1~X0~X2)))){\unicdbdjdcd}(r1\_xxreal\_0~(k18\_rvsum\_1~(k1\_glib\_003~k1\_numbers~\\
X0~X1))~(k18\_rvsum\_1~X0))))\end{array}
\label{hyp:ehcdpfhgmgjgcgpfadaddd}
\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}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v8\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X2 \in k4\_finseq\_1~(k9\_glib\_003~\\
X0~X1)){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(k1\_seq\_1~(k9\_glib\_003~X0~X1)~\\
X2)))))\end{array}
\label{hyp:ehcdidpfhgmgjgcgpfadaddd}
\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}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m4\_glib\_001~X2~X0~X1){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k9\_glib\_003~X0~X1))){\unicdcdcdhd}(k9\_glib\_003~X0~X2=k1\_glib\_003~k1\_numbers~\\
(k9\_glib\_003~X0~X1)~X3))))\end{array}
\label{hyp:ehbdidpfhgmgjgcgpfadaddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((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}(m3\_glib\_001~\\
X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_glib\_001~X2~X0~X1){\unicdbdjdcd}(m3\_glib\_001~X2~X0))\end{array}
\label{hyp:egehpfngedpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((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}((v1\_glib\_003~\\
X0){\unicdcdcdhd}(v7\_glib\_003~X0))))))){\unicdcdcdhd}(m3\_glib\_001~X1~X0)){\unicdbdjdcd}(m2\_finseq\_1~\\
(k9\_glib\_003~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgjdpfhgmgjgcgpfadaddd}
\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}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~X1~X0){\unicdbdjdcd}(k10\_glib\_003~\\
X0~X1=k18\_rvsum\_1~(k9\_glib\_003~X0~X1)))\end{array}
\label{hyp:egbdjdpfhgmgjgcgpfadaddd}
\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}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v8\_glib\_003~X0))))))){\unicdbdjdcd}((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}((v1\_glib\_003~\\
X0){\unicdcdcdhd}(v7\_glib\_003~X0)))))))\end{array}
\label{hyp:dgdgbdpfhgmgjgcgpfadaddd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfhgmgjgcgpfadaddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v8\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m4\_glib\_001~X2~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~(k10\_glib\_003~X0~X2)~(k10\_glib\_003~\\
X0~X1))))\end{array}$$
\end{theorem}
\end{document}
