\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\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t12\_arytm\_0 (TMQ7EdY4k8qy8r47KZhBDpik5PCbteKfBuZ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_arytm\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ k8\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_arytm\_3 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}r1\_xboole\_0~k2\_arytm\_2~(k2\_zfmisc\_1~(k1\_tarski~k11\_arytm\_3)~\\
k2\_arytm\_2)\end{array}
\label{hyp:ehfdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}((X0=k11\_arytm\_3){\unicdbdjdcd}(k8\_arytm\_2~X0~X1=k11\_arytm\_3)))\end{array}
\label{hyp:ehedpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh r1\_xboole\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in \\
X0){\unicdcdcdhd}(X2 \in X1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X2 .  (X2 \in X0){\unicdcdcdhd}(X2 \in X1)){\unicdcdcdhd}(r1\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ehddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{({{k11\_arytm\_3} \in {k2\_arytm\_2}})}{\unicdcdcdhd}{({{k12\_arytm\_3} \in {k2\_arytm\_2}})}}\label{hyp:ehcdadpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((((\\
X0 \in k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_arytm\_2)){\unicdbdjdcd}((X2=k2\_arytm\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k2\_arytm\_2){\unicdcdcdhd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=k8\_arytm\_2~X3~X4))))))){\unicdcdcdhd}((((X0 \in k2\_arytm\_2){\unicdcdcdhd}\\
(X1 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~k2\_arytm\_2)){\unicdbdjdcd}((X0=k6\_numbers){\unicdcdcdid}\\
((X2=k2\_arytm\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k2\_arytm\_2){\unicdcdcdhd}((X0=X3){\unicdcdcdhd}((X1=k4\_tarski~\\
k6\_numbers~X4){\unicdcdcdhd}(X2=k4\_tarski~k6\_numbers~(k8\_arytm\_2~X3~X4))))))))){\unicdcdcdhd}\\
((((X1 \in k2\_arytm\_2){\unicdcdcdhd}(X0 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~\\
k2\_arytm\_2)){\unicdbdjdcd}((X1=k6\_numbers){\unicdcdcdid}((X2=k2\_arytm\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k2\_arytm\_2){\unicdcdcdhd}\\
((X0=k4\_tarski~k6\_numbers~X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=k4\_tarski~k6\_numbers~\\
(k8\_arytm\_2~X4~X3))))))))){\unicdcdcdhd}((((X0 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~\\
k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~k2\_arytm\_2)){\unicdbdjdcd}\\
((X2=k2\_arytm\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k2\_arytm\_2){\unicdcdcdhd}((X0=k4\_tarski~k6\_numbers~\\
X3){\unicdcdcdhd}((X1=k4\_tarski~k6\_numbers~X4){\unicdcdcdhd}(X2=k8\_arytm\_2~X4~X3))))))){\unicdcdcdhd}\\
(\preoh (\preoh (X0 \in k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_arytm\_2)){\unicdcdcdhd}((\preoh (X0 \in k2\_arytm\_2){\unicdcdcdhd}\\
((X1 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~k2\_arytm\_2){\unicdcdcdhd}(X0{\unicdcdgdad}k6\_numbers))){\unicdcdcdhd}\\
((\preoh (X1 \in k2\_arytm\_2){\unicdcdcdhd}((X0 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~\\
k2\_arytm\_2){\unicdcdcdhd}(X1{\unicdcdgdad}k6\_numbers))){\unicdcdcdhd}((\preoh (X0 \in k2\_zfmisc\_1~(k1\_tarski~\\
k6\_numbers)~k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~\\
k2\_arytm\_2)){\unicdcdcdhd}(\preoh (X2=k2\_arytm\_0~X0~X1){\unicdbdjded}(X2=k6\_numbers))))))))))))\end{array}
\label{hyp:egcdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_numbers)){\unicdbdjdcd}(k2\_arytm\_0~X0~X1=k2\_arytm\_0~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfbgchjhehngpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfbgchjhehngpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}((X1=k6\_numbers){\unicdbdjdcd}(k2\_arytm\_0~X0~X1=k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
