\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{t91\_euclidlp (TMMES4kJKSuazhMYQLEiAz9eLtns7ZswcXW)}
\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 $ k5\_euclidlp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ 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\_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}(((X1 \in k4\_euclidlp~\\
X0~X2~X3~X4){\unicdcdcdhd}((X5 \in k4\_euclidlp~X0~X2~X3~X4){\unicdcdcdhd}(X6 \in k4\_euclidlp~X0~X2~\\
X3~X4))){\unicdbdjdcd}(r1\_tarski~(k4\_euclidlp~X0~X1~X5~X6)~(k4\_euclidlp~X0~X2~\\
X3~X4)))))))))\end{array}
\label{hyp:ehidddpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\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~(k5\_euclidlp~\\
X0))\end{array}
\label{hyp:ggdgddpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k5\_euclidlp~\\
X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(k1\_euclid~X0))))\end{array}
\label{hyp:egehpflgfdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(k5\_euclidlp~X0=ReplSep~\\
(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_euclid~X0))))~\\
({\uniddcgcg} X1 : \iota .  {\unicdcdaddd} X2 .  (m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~X0)){\unicdcdcdhd}(X1=k4\_euclidlp~\\
X0~X2~X3~X4))))~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egbdbdpffgfhdgmgjgegmgah}
\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:ehjdbdpffgfhdgmgjgegmgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~\\
(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~(k1\_zfmisc\_1~(k1\_euclid~X0))~\\
(k5\_euclidlp~X0)){\unicdbdjdcd}(((X1 \in X4){\unicdcdcdhd}((X2 \in X4){\unicdcdcdhd}(X3 \in X4))){\unicdbdjdcd}(r1\_tarski~\\
(k4\_euclidlp~X0~X1~X2~X3)~X4))))))\end{array}$$
\end{theorem}
\end{document}
