\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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\begin{document}
\title{t25\_hilbert3 (TMMeueXjztRX9em1hnNCCQEg1AhgJdfBJrC)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k16\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k15\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~X2){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X2))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3)))))){\unicdbdjdcd}(k16\_funct\_3~\\
X0~X1~X2~X3~X4~X5=k15\_funct\_3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdgdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~X1~X1){\unicdcdcdhd}((v3\_funct\_2~X3~X1~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X1~X1))))))){\unicdbdjdcd}((v1\_funct\_1~(k15\_funct\_3~X2~X3)){\unicdcdcdhd}(\\
(v1\_funct\_2~(k15\_funct\_3~X2~X3)~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~\\
X0~X1)){\unicdcdcdhd}(v3\_funct\_2~(k15\_funct\_3~X2~X3)~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~\\
X0~X1))))\end{array}
\label{hyp:ggdgedpfigjgmgcgfgchehdd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfigjgmgcgfgchehdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~X1~X1){\unicdcdcdhd}((v3\_funct\_2~X3~X1~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X1~X1)))))){\unicdbdjdcd}(v3\_funct\_2~(k16\_funct\_3~X0~X1~X0~X1~X2~\\
X3)~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
