\documentclass{article}
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\newtheorem{proposition}{Proposition}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t70\_euclid\_8 (TMZEgH3nKVNYEXnXhcUXz6w3PJ9Lkh8HCcT)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k23\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~\\
k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}(k23\_rvsum\_1~(k9\_euclid~np\_\_3~\\
X1~X0)~X2=k11\_binop\_2~X0~(k23\_rvsum\_1~X1~X2))))\end{array}
\label{hyp:ehgdidpffgfhdgmgjgegpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_2~X0~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_2~X1~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}(k23\_rvsum\_1~X0~\\
X1=k9\_binop\_2~(k9\_binop\_2~(k11\_binop\_2~(k1\_seq\_1~X0~np\_\_1)~(k1\_seq\_1~\\
X1~np\_\_1))~(k11\_binop\_2~(k1\_seq\_1~X0~np\_\_2)~(k1\_seq\_1~X1~np\_\_2)))~\\
(k11\_binop\_2~(k1\_seq\_1~X0~np\_\_3)~(k1\_seq\_1~X1~np\_\_3))))\end{array}
\label{hyp:mghdpffgfhdgmgjgegpfid}
\end{equation}
\begin{theorem}\label{thm:ehhdadpffgfhdgmgjgegpfid}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~\\
k1\_numbers~(k1\_euclid~np\_\_3)){\unicdbdjdcd}(k23\_rvsum\_1~(k9\_euclid~np\_\_3~\\
X1~X0)~X2=k11\_binop\_2~X0~(k9\_binop\_2~(k9\_binop\_2~(k11\_binop\_2~\\
(k1\_seq\_1~X1~np\_\_1)~(k1\_seq\_1~X2~np\_\_1))~(k11\_binop\_2~(k1\_seq\_1~\\
X1~np\_\_2)~(k1\_seq\_1~X2~np\_\_2)))~(k11\_binop\_2~(k1\_seq\_1~X1~np\_\_3)~\\
(k1\_seq\_1~X2~np\_\_3))))))\end{array}$$
\end{theorem}
\end{document}
