\documentclass{article}
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\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{t11\_euclid\_7 (TMLf4Z6Fic4q41vaKQTj4DpP7Pbwp8pDPbJ)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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\_funct\_1~k1\_xboole\_0){\unicdcdcdhd}((v1\_funct\_2~k1\_xboole\_0~\\
X0~k1\_xboole\_0){\unicdcdcdhd}(m1\_subset\_1~k1\_xboole\_0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_xboole\_0))))\end{array}
\label{hyp:ehbdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v5\_relat\_1~X1~\\
X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_funct\_2~X1~X0~\\
X0){\unicdcdcdhd}(v3\_funct\_2~X1~X0~X0)))))))\end{array}
\label{hyp:chdgcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0))))\end{array}
\label{hyp:dgdghdpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpffgfhdgmgjgegpfhd}
$$\begin{array}{c}(v1\_funct\_1~k1\_xboole\_0){\unicdcdcdhd}((v1\_funct\_2~k1\_xboole\_0~k1\_xboole\_0~\\
k1\_xboole\_0){\unicdcdcdhd}((v3\_funct\_2~k1\_xboole\_0~k1\_xboole\_0~k1\_xboole\_0){\unicdcdcdhd}\\
(m1\_subset\_1~k1\_xboole\_0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_xboole\_0~\\
k1\_xboole\_0)))))\end{array}$$
\end{theorem}
\end{document}
