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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t21\_glib\_003 (TMUncjww8vgpiqb9kYmRXoAPZPiUGQWhUME)}
\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 $ v7\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k8\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{{k18\_rvsum\_1}~{({{k6\_finseq\_1}~{k1\_numbers}})}}={k6\_numbers}}\label{hyp:ehhdcdpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m3\_glib\_001~X1~X0){\unicdbdjdcd}((v3\_glib\_001~X1~X0){\unicdbdjdcd}(k8\_glib\_003~\\
X0~X1=k1\_xboole\_0)))\end{array}
\label{hyp:ehbdcdpfhgmgjgcgpfadaddd}
\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}(k9\_glib\_003~\\
X0~X1=k8\_glib\_003~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfhgmgjgcgpfadaddd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_xboole\_0}~{({{k6\_finseq\_1}~{X0}})}}}\label{hyp:ggdgfdpfggjgogdhfgbhpfbd}
\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}
\begin{theorem}\label{thm:ehcdbdpfhgmgjgcgpfadaddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~X1~X0){\unicdbdjdcd}((v3\_glib\_001~\\
X1~X0){\unicdbdjdcd}(k10\_glib\_003~X0~X1=k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
