\documentclass{article}
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\begin{document}
\title{t5\_transgeo (TMMc5rudHCn5r4XgojmUorkf3tbLYJHKtrT)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_transgeo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\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~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X3~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X0~(k1\_transgeo~X0~X2~X1)~\\
(k1\_transgeo~X0~X2~X3)){\unicdbdjdcd}(r2\_funct\_2~X0~X0~X1~X3)))))\end{array}
\label{hyp:mghdpfehchbgogdhhgfgpg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\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~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X3~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X0~(k1\_transgeo~X0~X2~X1)~\\
(k1\_transgeo~X0~X3~X1)){\unicdbdjdcd}(r2\_funct\_2~X0~X0~X2~X3)))))\end{array}
\label{hyp:mggdpfehchbgogdhhgfgpg}
\end{equation}
\begin{theorem}\label{thm:ehfdpfehchbgogdhhgfgpg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~X0~X0){\unicdcdcdhd}((v3\_funct\_2~X3~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}(((r2\_funct\_2~X0~X0~(k1\_transgeo~X0~X2~\\
X1)~(k1\_transgeo~X0~X2~X3)){\unicdcdcdid}(r2\_funct\_2~X0~X0~(k1\_transgeo~X0~X1~\\
X2)~(k1\_transgeo~X0~X3~X2))){\unicdbdjdcd}(r2\_funct\_2~X0~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
