\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t88\_valued\_2 (TMRToasWa91cYY35gLRA7bVXtvtJBi6fstV)}
\maketitle
Let $ v1\_valued\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k84\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k73\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (v1\_valued\_2~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (v1\_valued\_2~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_valued\_2~X5){\unicdbdjdcd}(\\
{\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X3)))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X4)))){\unicdbdjdcd}({\unicdcdadad} X8 .  ((v1\_funct\_1~X8){\unicdcdcdhd}(m1\_subset\_1~\\
X8~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X5)))){\unicdbdjdcd}(k84\_valued\_2~X0~(k3\_xboole\_0~\\
X1~X2)~X3~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~X4)~(k1\_valued\_2~\\
X5)))~X6~(k73\_valued\_2~X1~X2~X4~X5~X7~X8)=k73\_valued\_2~(k3\_xboole\_0~\\
X0~X1)~(k3\_xboole\_0~X0~X2)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X3)~(k1\_valued\_2~X4)))~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X3)~(k1\_valued\_2~X5)))~(k84\_valued\_2~X0~X1~X3~X4~X6~X7)~(k84\_valued\_2~\\
X0~X2~X3~X5~X6~X8)))))))\end{array}
\label{hyp:ehidhdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_valued\_2~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v1\_valued\_2~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3)))){\unicdbdjdcd}(k84\_valued\_2~\\
X0~X1~X2~X3~X4~X5=k84\_valued\_2~X1~X0~X3~X2~X5~X4))))\end{array}
\label{hyp:ehidddpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_valued\_2}~{({{k2\_valued\_2}~{X0}})}}}\label{hyp:ggdgcdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((v1\_valued\_2~X2){\unicdcdcdhd}((v1\_valued\_2~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3))))))){\unicdbdjdcd}((v1\_funct\_1~(k73\_valued\_2~\\
X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~(k73\_valued\_2~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_xboole\_0~X0~X1)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X2)~(k1\_valued\_2~X3)))))))\end{array}
\label{hyp:egehpflghdddpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehididpfghbgmgfhfgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (v1\_valued\_2~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (v1\_valued\_2~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_valued\_2~X5){\unicdbdjdcd}(\\
{\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X3)))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X4)))){\unicdbdjdcd}({\unicdcdadad} X8 .  ((v1\_funct\_1~X8){\unicdcdcdhd}(m1\_subset\_1~\\
X8~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X5)))){\unicdbdjdcd}(k84\_valued\_2~(k3\_xboole\_0~\\
X1~X2)~X0~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~X4)~(k1\_valued\_2~\\
X5)))~X3~(k73\_valued\_2~X1~X2~X4~X5~X7~X8)~X6=k73\_valued\_2~(k3\_xboole\_0~\\
X1~X0)~(k3\_xboole\_0~X2~X0)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X4)~(k1\_valued\_2~X3)))~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X5)~(k1\_valued\_2~X3)))~(k84\_valued\_2~X1~X0~X4~X3~X7~X6)~(k84\_valued\_2~\\
X2~X0~X5~X3~X8~X6)))))))\end{array}$$
\end{theorem}
\end{document}
