\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t6\_polyeq\_3 (TMEzf3a62ifcuyjZFRDCz6Sn84QiF5RXRn1)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_polyeq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (v1\_xreal\_0~X6){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (v1\_xreal\_0~X7){\unicdbdjdcd}(({\unicdcdadad} X8 .  (v1\_xreal\_0~X8){\unicdbdjdcd}(k7\_polyeq\_1~\\
X0~X1~X2~X3~X8=k7\_polyeq\_1~X4~X5~X6~X7~X8)){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((\\
X2=X6){\unicdcdcdhd}(X3=X7))))))))))))\end{array}
\label{hyp:ehbdcdpfahpgmgjhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfchfgbgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfahpgmgjhfgbhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}(({\unicdcdadad} X8 .  \\
(v1\_xcmplx\_0~X8){\unicdbdjdcd}(k7\_polyeq\_1~X0~X1~X2~X3~X8=k7\_polyeq\_1~X4~X5~X6~\\
X7~X8)){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7))))))))))))\end{array}$$
\end{theorem}
\end{document}
