\documentclass{article}
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\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\unicdbdjded{\Leftrightarrow}
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\begin{document}
\title{l66\_hilbert1 (TMPocHJojvhga2BUZvPcL887ADXHENH14P8)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_hilbert1 : {\iota}$ be given.
Let $ k3\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_hilbert1 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_hilbert1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_hilbert1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}(k3\_hilbert1~\\
(k3\_hilbert1~X0~X1)~(k3\_hilbert1~(k4\_hilbert1~X2~X0)~(k4\_hilbert1~\\
X2~X1)) \in k6\_hilbert1)))\end{array}
\label{hyp:ehedgdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}(k3\_hilbert1~\\
(k4\_hilbert1~(k4\_hilbert1~X0~X1)~X2)~X1 \in k6\_hilbert1)))\end{array}
\label{hyp:mggdfdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_hilbert1}~{k6\_hilbert1}}\label{hyp:ggdgedpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_hilbert1}}~{({{k1\_zfmisc\_1}~{k1\_hilbert1}})}}\label{hyp:egehpflggdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_hilbert1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_hilbert1)){\unicdbdjdcd}(m1\_subset\_1~(k4\_hilbert1~X0~X1)~k1\_hilbert1)\end{array}
\label{hyp:egehpflgedpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_hilbert1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_hilbert1)){\unicdbdjdcd}(m1\_subset\_1~(k3\_hilbert1~X0~X1)~k1\_hilbert1)\end{array}
\label{hyp:egehpflgddpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}((v6\_hilbert1~\\
X0){\unicdbdjded}((k2\_hilbert1 \in X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_hilbert1){\unicdbdjdcd}((k3\_hilbert1~X1~(k3\_hilbert1~X2~X1) \in X0){\unicdcdcdhd}((k3\_hilbert1~\\
(k3\_hilbert1~X1~(k3\_hilbert1~X2~X3))~(k3\_hilbert1~(k3\_hilbert1~\\
X1~X2)~(k3\_hilbert1~X1~X3)) \in X0){\unicdcdcdhd}((k3\_hilbert1~(k4\_hilbert1~X1~\\
X2)~X1 \in X0){\unicdcdcdhd}((k3\_hilbert1~(k4\_hilbert1~X1~X2)~X2 \in X0){\unicdcdcdhd}((k3\_hilbert1~\\
X1~(k3\_hilbert1~X2~(k4\_hilbert1~X1~X2)) \in X0){\unicdcdcdhd}(((X1 \in X0){\unicdcdcdhd}(k3\_hilbert1~\\
X1~X2 \in X0)){\unicdbdjdcd}(X2 \in X0))))))))))))\end{array}
\label{hyp:egbdadpfigjgmgcgfgchehbd}
\end{equation}
\begin{theorem}\label{thm:mggdgdpfigjgmgcgfgchehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}(k3\_hilbert1~\\
(k4\_hilbert1~(k4\_hilbert1~(k4\_hilbert1~X0~X1)~X2)~(k4\_hilbert1~\\
(k4\_hilbert1~X0~X1)~X2))~(k4\_hilbert1~(k4\_hilbert1~(k4\_hilbert1~\\
X0~X1)~X2)~X1) \in k6\_hilbert1)))\end{array}$$
\end{theorem}
\end{document}
