\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{t104\_euclidlp (TMYc1uoRhDrHS5tgvU1XhWxknmWnkMwDSLs)}
\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 $ k1\_euclidlp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_euclid\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_euclidlp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_euclidlp : {{\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 $ k2\_euclid\_4 : {{\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\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_euclid~\\
X0))~(k5\_euclidlp~X0)){\unicdbdjdcd}(((X1 \in X3){\unicdcdcdhd}(X2 \in X3)){\unicdbdjdcd}(r1\_tarski~(k2\_euclid\_4~\\
X0~X1~X2)~X3)))))\end{array}
\label{hyp:ehjdfdpffgfhdgmgjgegmgah}
\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}\\
(\preoh (v1\_euclid\_4~X1~X0){\unicdcdcdhd}((v1\_euclid\_4~X2~X0){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}(\preoh (X3 \in X1){\unicdcdcdhd}(\preoh X3 \in X2))))))))\end{array}
\label{hyp:ehhdjdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\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}\\
((\preoh (\preoh r1\_xboole\_0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~\\
(k1\_euclid~X0)){\unicdbdjdcd}(\preoh (X3 \in X1){\unicdcdcdhd}(X3 \in X2)))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X3 .  (m2\_finseq\_2~\\
X3~k1\_numbers~(k1\_euclid~X0)){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}(X3 \in X2))){\unicdcdcdhd}(r1\_xboole\_0~\\
X1~X2)))))\end{array}
\label{hyp:ehedjdpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~\\
k1\_numbers~(k1\_euclid~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~\\
(k1\_euclid~X0)){\unicdbdjdcd}(((v1\_euclid\_4~X1~X0){\unicdcdcdhd}((X2 \in X1){\unicdcdcdhd}(X3 \in X1))){\unicdbdjdcd}(\\
(X2=X3){\unicdcdcdid}(X1=k2\_euclid\_4~X0~X2~X3))))))\end{array}
\label{hyp:ehddadpffgfhdgmgjgegmgah}
\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 .  (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 (\preoh X1 \in X2){\unicdcdcdhd}((v1\_euclid\_4~\\
X2~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_euclid~X0))~\\
(k5\_euclidlp~X0)){\unicdbdjdcd}(\preoh (X1 \in X3){\unicdcdcdhd}((r1\_tarski~X2~X3){\unicdcdcdhd}(v1\_euclidlp~\\
X3~X0))))))))\end{array}
\label{hyp:ehbdadadpffgfhdgmgjgegmgah}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\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~(k1\_euclidlp~\\
X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(k1\_euclid~X0))))\end{array}
\label{hyp:egehpflgbdpffgfhdgmgjgegmgah}
\end{equation}
\begin{theorem}\label{thm:ehbdadedpffgfhdgmgjgegmgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}\\
(\preoh (v1\_euclid\_4~X1~X0){\unicdcdcdhd}((v1\_euclid\_4~X2~X0){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((\preoh r1\_xboole\_0~\\
X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_euclid~X0))~\\
(k5\_euclidlp~X0)){\unicdbdjdcd}(\preoh (r1\_tarski~X1~X3){\unicdcdcdhd}((r1\_tarski~X2~X3){\unicdcdcdhd}(v1\_euclidlp~\\
X3~X0))))))))))\end{array}$$
\end{theorem}
\end{document}
