\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t10\_euclid\_7 (TMaNSR7PLb2kd63hCJdH4oihnkUA7JgjKpt)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_finseq\_7 : {{\iota}{\unicdbdjdcd}{{\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 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\\
((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k3\_finseq\_1~X1)){\unicdcdcdhd}(\\
(r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_finseq\_1~X1))))){\unicdbdjdcd}\\
((k1\_funct\_1~(k2\_finseq\_7~X0~X1~X2~X3)~X2=k1\_funct\_1~X1~X3){\unicdcdcdhd}(k1\_funct\_1~\\
(k2\_finseq\_7~X0~X1~X2~X3)~X3=k1\_funct\_1~X1~X2))))))\end{array}
\label{hyp:mgcdddpfggjgogdhfgbhpfhd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpffgfhdgmgjgegpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~X2){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k3\_finseq\_1~X3)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~\\
X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~(k3\_finseq\_1~X3))))){\unicdbdjdcd}((k1\_funct\_1~(k2\_finseq\_7~\\
X2~X3~X0~X1)~X0=k1\_funct\_1~X3~X1){\unicdcdcdhd}(k1\_funct\_1~(k2\_finseq\_7~X2~X3~\\
X0~X1)~X1=k1\_funct\_1~X3~X0))))))\end{array}$$
\end{theorem}
\end{document}
