\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{l7\_group\_9 (TMcSC37e8BU7qnkbY5jbqgDcCNvRoyDuVXN)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjdcd}((v1\_funct\_1~(k2\_funcop\_1~\\
X0~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_funcop\_1~X0~X2)~X0~X1){\unicdcdcdhd}(m1\_subset\_1~(\\
k2\_funcop\_1~X0~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))\end{array}
\label{hyp:ehedfdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k4\_funct\_7}~{X0}}~{k1\_xboole\_0}}={{k6\_partfun1}~{X0}}}}\label{hyp:ehddjdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k4\_relat\_1}~{X0}} \in {{{k1\_funct\_2}~{X0}}~{X0}}}}\label{hyp:ehbdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k1\_funct\_2}~{X0}}~{X1}}={{k4\_card\_3}~{({{{k7\_funcop\_1}~{X0}}~{X1}})}}}}}\label{hyp:ehbdbdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k7\_funcop\_1}~{X0}}~{X1}}={{{k2\_funcop\_1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_funct\_1~(k7\_funcop\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k7\_funcop\_1~X0~X1)~X0~(k1\_tarski~X1)){\unicdcdcdhd}(m1\_subset\_1~(k7\_funcop\_1~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(k1\_tarski~X1)))))\end{array}
\label{hyp:egehpflghdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_funcop\_1~X0~X1=k2\_zfmisc\_1~X0~(k1\_tarski~\\
X1)\end{array}
\label{hyp:egcdpfggfhogdgpgahpfbd}
\end{equation}
\begin{theorem}\label{thm:mghdpfhgchpgfhahpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_funct\_1~(k2\_zfmisc\_1~X0~(k1\_tarski~\\
(k6\_partfun1~X1)))){\unicdcdcdhd}((v1\_funct\_2~(k2\_zfmisc\_1~X0~(k1\_tarski~\\
(k6\_partfun1~X1)))~X0~(k1\_funct\_2~X1~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_zfmisc\_1~\\
X0~(k1\_tarski~(k6\_partfun1~X1)))~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
(k1\_funct\_2~X1~X1)))))\end{array}$$
\end{theorem}
\end{document}
