\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\begin{document}
\title{t26\_euclidlp (TMGv9wJN3bEPoZgnXuH5kPkQkbDVUs3u9ax)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~\\
(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_finseq\_2~X5~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m2\_finseq\_2~X6~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}(k8\_euclid~X0~(k7\_euclid~\\
X0~(k7\_euclid~X0~X1~X2)~X3)~(k7\_euclid~X0~(k7\_euclid~X0~X4~X5)~X6)=\\
k7\_euclid~X0~(k7\_euclid~X0~(k8\_euclid~X0~X1~X4)~(k8\_euclid~X0~X2~X5))~\\
(k8\_euclid~X0~X3~X6))))))))\end{array}
\label{hyp:ehbdjdpffgfhdgmgjgegmgah}
\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~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~X2)){\unicdbdjdcd}((k9\_euclid~X2~X3~(\\
k9\_real\_1~X0~X1)=k7\_euclid~X2~(k9\_euclid~X2~X3~X0)~(k9\_euclid~X2~\\
X3~(k1\_real\_1~X1))){\unicdcdcdhd}((k9\_euclid~X2~X3~(k9\_real\_1~X0~X1)=k7\_euclid~\\
X2~(k9\_euclid~X2~X3~X0)~(k6\_euclid~X2~(k9\_euclid~X2~X3~X1))){\unicdcdcdhd}(k9\_euclid~\\
X2~X3~(k9\_real\_1~X0~X1)=k8\_euclid~X2~(k9\_euclid~X2~X3~X0)~(k9\_euclid~\\
X2~X3~X1)))))))\end{array}
\label{hyp:ehbdbdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k1\_euclid~X0)){\unicdcdcdhd}(v1\_xreal\_0~X2))){\unicdbdjdcd}(m2\_finseq\_2~(k9\_euclid~\\
X0~X1~X2)~k1\_numbers~(k1\_euclid~X0))\end{array}
\label{hyp:egehpflgjdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{m1\_finseq\_2}~{({{k1\_euclid}~{X0}})}}~{k1\_numbers}})}}}\label{hyp:egehpflgbdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpffgfhdgmgjgegmgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_finseq\_2~X7~k1\_numbers~(k1\_euclid~\\
X6)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m2\_finseq\_2~X8~k1\_numbers~(k1\_euclid~X6)){\unicdbdjdcd}\\
({\unicdcdadad} X9 .  (m2\_finseq\_2~X9~k1\_numbers~(k1\_euclid~X6)){\unicdbdjdcd}(k8\_euclid~\\
X6~(k7\_euclid~X6~(k7\_euclid~X6~(k9\_euclid~X6~X7~X0)~(k9\_euclid~X6~\\
X8~X1))~(k9\_euclid~X6~X9~X2))~(k7\_euclid~X6~(k7\_euclid~X6~(k9\_euclid~\\
X6~X7~X3)~(k9\_euclid~X6~X8~X4))~(k9\_euclid~X6~X9~X5))=k7\_euclid~X6~\\
(k7\_euclid~X6~(k9\_euclid~X6~X7~(k9\_real\_1~X0~X3))~(k9\_euclid~X6~X8~\\
(k9\_real\_1~X1~X4)))~(k9\_euclid~X6~X9~(k9\_real\_1~X2~X5))))))))))))\end{array}$$
\end{theorem}
\end{document}
