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\begin{document}
\title{t86\_valued\_2 (TMYzNYAfZ9p9RSzGHodnPffG9BguhRtyukZ)}
\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 $ k2\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_valued\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_valued\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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~(k2\_valued\_2~(k1\_valued\_2~X2))~X3~(k16\_valued\_2~X0~X2~X4)~X5=\\
k16\_valued\_2~(k3\_xboole\_0~X0~X1)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X2)~(k1\_valued\_2~X3)))~(k84\_valued\_2~X0~X1~X2~X3~X4~X5)))))\end{array}
\label{hyp:ehidfdpfghbgmgfhfgegpfcd}
\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 .  ((v1\_valued\_2~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k16\_valued\_2~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k16\_valued\_2~X0~X1~X2)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(k2\_valued\_2~(k1\_valued\_2~X1))))))\end{array}
\label{hyp:egehpflgbdgdpfghbgmgfhfgegpfcd}
\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:ehidgdpfghbgmgfhfgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_valued\_2~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v1\_valued\_2~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X2)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3)))){\unicdbdjdcd}(k84\_valued\_2~\\
X0~X1~X2~(k2\_valued\_2~(k1\_valued\_2~X3))~X4~(k16\_valued\_2~X1~X3~X5)=\\
k16\_valued\_2~(k3\_xboole\_0~X0~X1)~(k2\_valued\_2~(k3\_xboole\_0~(k1\_valued\_2~\\
X2)~(k1\_valued\_2~X3)))~(k84\_valued\_2~X0~X1~X2~X3~X4~X5)))))\end{array}$$
\end{theorem}
\end{document}
