\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=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t88\_euclidlp (TMcqSrZPECQ27LESxPoJvg85AvFfigkhUfu)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\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.
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}(k4\_euclidlp~X0~X1~X2~X3=ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m2\_finseq\_2~\\
X4~k1\_numbers~(k1\_euclid~X0)))~({\uniddcgcg} X4 : \iota .  {\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X7 .  \\
(m1\_subset\_1~X7~k1\_numbers){\unicdcdcdhd}((k7\_real\_1~(k7\_real\_1~X5~X6)~X7=\\
np\_\_1){\unicdcdcdhd}(X4=k7\_euclid~X0~(k7\_euclid~X0~(k9\_euclid~X0~X1~X5)~(k9\_euclid~\\
X0~X2~X6))~(k9\_euclid~X0~X3~X7))))))~({\uniddcgcg} X4 : \iota .  X4)))))\end{array}
\label{hyp:egjdpffgfhdgmgjgegmgah}
\end{equation}
\begin{theorem}\label{thm:ehididpffgfhdgmgjgegmgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~\\
(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}\\
((X1 \in k4\_euclidlp~X0~X2~X3~X4){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~\\
X7~k1\_numbers){\unicdcdcdhd}((k7\_real\_1~(k7\_real\_1~X5~X6)~X7=np\_\_1){\unicdcdcdhd}(X1=k7\_euclid~\\
X0~(k7\_euclid~X0~(k9\_euclid~X0~X2~X5)~(k9\_euclid~X0~X3~X6))~(k9\_euclid~\\
X0~X4~X7)))))))))))\end{array}$$
\end{theorem}
\end{document}
