\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{t93\_euclidlp (TMbRyoYzoMe4uuG8fNKFp6k6PVz3K1WZWge)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\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\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_euclidlp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r3\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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\_subset\_1~X4~(k1\_zfmisc\_1~(k1\_euclid~X0))~\\
(k5\_euclidlp~X0)){\unicdbdjdcd}(((X1 \in X4){\unicdcdcdhd}((X2 \in X4){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(r3\_euclidlp~\\
X0~(k8\_euclid~X0~X2~X1)~(k8\_euclid~X0~X3~X1))))){\unicdbdjdcd}(X4=k4\_euclidlp~\\
X0~X1~X2~X3))))))\end{array}
\label{hyp:ehjdcdpffgfhdgmgjgegmgah}
\end{equation}
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}((X1 \in k4\_euclidlp~X0~X1~X2~X3){\unicdcdcdhd}((X2 \in k4\_euclidlp~X0~X1~X2~X3){\unicdcdcdhd}\\
(X3 \in k4\_euclidlp~X0~X1~X2~X3))))))\end{array}
\label{hyp:ehidcdpffgfhdgmgjgegmgah}
\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 .  {\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){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\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 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_euclid~X0))){\unicdbdjdcd}((v1\_euclidlp~X1~X0){\unicdbdjded}({\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}((r3\_euclidlp~X0~(k8\_euclid~X0~X3~X2)~(k8\_euclid~\\
X0~X4~X2)){\unicdcdcdhd}(X1=k4\_euclidlp~X0~X2~X3~X4)))))))\end{array}
\label{hyp:egbdadpffgfhdgmgjgegmgah}
\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:ehjdddpffgfhdgmgjgegmgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k5\_euclidlp~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k5\_euclidlp~X0)){\unicdbdjdcd}\\
(((v1\_euclidlp~X1~X0){\unicdcdcdhd}(r1\_tarski~X1~X2)){\unicdbdjdcd}(X1=X2))))\end{array}$$
\end{theorem}
\end{document}
