\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l26\_hilbert1 (TMGviArjg7jsZhBVoNBNQ3riFac4SaBqNim)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_hilbert1 : {\iota}$ be given.
Let $ v6\_hilbert1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_hilbert1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_hilbert1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}\\
(((X1 \in k5\_hilbert1~X0){\unicdcdcdhd}(k3\_hilbert1~X1~X2 \in k5\_hilbert1~X0)){\unicdbdjdcd}(\\
X2 \in k5\_hilbert1~X0))))\end{array}
\label{hyp:ehhdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~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~X1~X2)~X2 \in k5\_hilbert1~X0)))\end{array}
\label{hyp:ehgdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~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~X1~X2)~X1 \in k5\_hilbert1~X0)))\end{array}
\label{hyp:ehfdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}\\
(k3\_hilbert1~X1~(k3\_hilbert1~X2~X1) \in k5\_hilbert1~X0)))\end{array}
\label{hyp:ehedpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}({\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~(k3\_hilbert1~\\
X1~(k3\_hilbert1~X2~X3))~(k3\_hilbert1~(k3\_hilbert1~X1~X2)~(k3\_hilbert1~\\
X1~X3)) \in k5\_hilbert1~X0))))\end{array}
\label{hyp:ehddpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}\\
(k3\_hilbert1~X1~(k3\_hilbert1~X2~(k4\_hilbert1~X1~X2)) \in k5\_hilbert1~\\
X0)))\end{array}
\label{hyp:ehcdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}(k2\_hilbert1 \in \\
k5\_hilbert1~X0)\end{array}
\label{hyp:ehbdpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k5\_hilbert1~X0)~(k1\_zfmisc\_1~k1\_hilbert1))\end{array}
\label{hyp:egehpflgfdpfigjgmgcgfgchehbd}
\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:mgcdgdpfigjgmgcgfgchehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}(v6\_hilbert1~\\
(k5\_hilbert1~X0))\end{array}$$
\end{theorem}
\end{document}
