\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t4\_cayley (TMcHjzMbH7xnGNgDE2mRFmhYjghmzWvLUJu)}
\maketitle
Let $ k1\_cayley : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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\_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}
{{np\_\_1}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehedjdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1 \in k1\_cayley~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0))))))\end{array}
\label{hyp:ehbdpfdgbgjhmgfgjh}
\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 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k1\_cayley~X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  (v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))))~({\uniddcgcg} X1 : \iota .  True)~(\\
{\uniddcgcg} X1 : \iota .  X1)\end{array}
\label{hyp:egbdpfdgbgjhmgfgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:dgdgddpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfdgbgjhmgfgjh}
${{{k1\_cayley}~{k1\_xboole\_0}}={np\_\_1}}$.
\end{theorem}
\end{document}
