\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{t57\_euclid\_8 (TMNg3CJTbVU1VHoo3F76XQpDgTCn7HmhKa1)}
\maketitle
Let $ v1\_funct\_1 : {{\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 $ k1\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k6\_euclid\_8 : {{\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 $ k2\_euclid\_8 : {\iota}$ be given.
Let $ k3\_euclid\_8 : {\iota}$ be given.
Let $ k4\_euclid\_8 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(k3\_funct\_2~\\
k1\_numbers~(k1\_euclid~np\_\_3)~(k6\_euclid\_8~X0~X1~X2)~X3=k7\_euclid~\\
np\_\_3~(k7\_euclid~np\_\_3~(k9\_euclid~np\_\_3~k2\_euclid\_8~(k1\_seq\_1~\\
X0~X3))~(k9\_euclid~np\_\_3~k3\_euclid\_8~(k1\_seq\_1~X1~X3)))~(k9\_euclid~\\
np\_\_3~k4\_euclid\_8~(k1\_seq\_1~X2~X3))))))\end{array}
\label{hyp:ehedidpffgfhdgmgjgegpfid}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpffgfhdgmgjgegpfid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}\\
(((k1\_seq\_1~X0~X6=k1\_seq\_1~X1~X7){\unicdcdcdhd}((k1\_seq\_1~X2~X6=k1\_seq\_1~X3~\\
X7){\unicdcdcdhd}(k1\_seq\_1~X4~X6=k1\_seq\_1~X5~X7))){\unicdbdjdcd}(k3\_funct\_2~k1\_numbers~\\
(k1\_euclid~np\_\_3)~(k6\_euclid\_8~X0~X2~X4)~X6=k3\_funct\_2~k1\_numbers~\\
(k1\_euclid~np\_\_3)~(k6\_euclid\_8~X1~X3~X5)~X7)))))))))\end{array}$$
\end{theorem}
\end{document}
