\documentclass{article}
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\newtheorem{proposition}{Proposition}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t6\_euclid\_5 (TMUg3iu7JFbEuUhZoR8ow6Nt7oFJk2UCNA4)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k4\_euclid\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}\\
(k3\_rlvect\_1~(k15\_euclid~np\_\_3)~X0~X1=k4\_euclid\_5~(k7\_real\_1~\\
(k1\_euclid\_5~X0)~(k1\_euclid\_5~X1))~(k7\_real\_1~(k2\_euclid\_5~X0)~\\
(k2\_euclid\_5~X1))~(k7\_real\_1~(k3\_euclid\_5~X0)~(k3\_euclid\_5~X1))))\end{array}
\label{hyp:ehfdpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\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}((k1\_euclid\_5~\\
(k4\_euclid\_5~X0~X1~X2)=X0){\unicdcdcdhd}((k2\_euclid\_5~(k4\_euclid\_5~X0~X1~X2)=\\
X1){\unicdcdcdhd}(k3\_euclid\_5~(k4\_euclid\_5~X0~X1~X2)=X2)))))\end{array}
\label{hyp:ehcdpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}((v1\_xreal\_0~\\
X1){\unicdcdcdhd}(v1\_xreal\_0~X2))){\unicdbdjdcd}(m1\_subset\_1~(k4\_euclid\_5~X0~X1~X2)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_3)))\end{array}
\label{hyp:egehpflgedpffgfhdgmgjgegpffd}
\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:ehgdpffgfhdgmgjgegpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}(k3\_rlvect\_1~(k15\_euclid~\\
np\_\_3)~(k4\_euclid\_5~X0~X1~X2)~(k4\_euclid\_5~X3~X4~X5)=k4\_euclid\_5~\\
(k7\_real\_1~X0~X3)~(k7\_real\_1~X1~X4)~(k7\_real\_1~X2~X5)))))))\end{array}$$
\end{theorem}
\end{document}
