\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{t80\_euclidlp (TMNb7YYhSDfJndrkCw1t7b9ortGpKAMLRzb)}
\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 $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_euclidlp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r6\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r5\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_euclid\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_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\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}(\preoh (v1\_euclid\_4~X2~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}\\
(\preoh (X1 \in X3){\unicdcdcdhd}(r5\_euclidlp~X0~X3~X2))))))\end{array}
\label{hyp:ehhdcdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}\\
((r6\_euclidlp~X0~X1~X2){\unicdbdjdcd}((v1\_euclid\_4~X1~X0){\unicdcdcdhd}(v1\_euclid\_4~X2~X0)))))\end{array}
\label{hyp:ehgdhdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~\\
X0)){\unicdbdjdcd}(((r6\_euclidlp~X0~X1~X2){\unicdcdcdhd}(r5\_euclidlp~X0~X2~X3)){\unicdbdjdcd}(r6\_euclidlp~\\
X0~X1~X3)))))\end{array}
\label{hyp:ehgdbdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(k1\_euclidlp~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_euclidlp~\\
X0)))){\unicdbdjdcd}((r6\_euclidlp~X0~X1~X2){\unicdbdjdcd}(r6\_euclidlp~X0~X2~X1))\end{array}
\label{hyp:dhjhngngfgehchjhpfchgdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(k1\_euclidlp~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_euclidlp~\\
X0)))){\unicdbdjdcd}((r5\_euclidlp~X0~X1~X2){\unicdbdjdcd}(r5\_euclidlp~X0~X2~X1))\end{array}
\label{hyp:dhjhngngfgehchjhpfchfdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_euclidlp~\\
X0))\end{array}
\label{hyp:ggdgbdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k1\_euclidlp~\\
X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(k1\_euclid~X0))))\end{array}
\label{hyp:egehpflgbdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidadpffgfhdgmgjgegmgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}(\preoh (r6\_euclidlp~\\
X0~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~(k1\_zfmisc\_1~(k1\_euclid~\\
X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}(\preoh (X1 \in X4){\unicdcdcdhd}((r6\_euclidlp~X0~X4~X3){\unicdcdcdhd}(r5\_euclidlp~\\
X0~X4~X2))))))))\end{array}$$
\end{theorem}
\end{document}
