\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}
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\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{t67\_euclidlp (TMQuZ5fgYLuZvFe13VH6QVz5uBx5LMWGsnK)}
\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 $ r6\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_euclid\_4 : {{\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 $ k8\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_euclid\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r4\_euclidlp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\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}((X1=X2){\unicdbdjded}(k8\_euclid~X0~X1~X2=k5\_euclid~X0))))\end{array}
\label{hyp:ehjdpffgfhdgmgjgegmgah}
\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 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k1\_euclid~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_euclid~X0)))){\unicdbdjdcd}(m2\_finseq\_2~\\
(k8\_euclid~X0~X1~X2)~k1\_numbers~(k1\_euclid~X0))\end{array}
\label{hyp:egehpflgidpffgfhdgmgjgeg}
\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}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{m1\_finseq\_2}~{({{k1\_euclid}~{X0}})}}~{k1\_numbers}})}}}\label{hyp:egehpflgbdpffgfhdgmgjgeg}
\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){\unicdbdjded}({\unicdcdaddd} X3 .  (m2\_finseq\_2~X3~k1\_numbers~\\
(k1\_euclid~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_finseq\_2~X4~k1\_numbers~(k1\_euclid~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_finseq\_2~X5~k1\_numbers~(k1\_euclid~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m2\_finseq\_2~X6~k1\_numbers~(k1\_euclid~X0)){\unicdcdcdhd}((X1=\\
k2\_euclid\_4~X0~X3~X4){\unicdcdcdhd}((X2=k2\_euclid\_4~X0~X5~X6){\unicdcdcdhd}(r4\_euclidlp~\\
X0~(k8\_euclid~X0~X4~X3)~(k8\_euclid~X0~X6~X5)))))))))))\end{array}
\label{hyp:egidpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(k1\_euclidlp~X0=ReplSep2~\\
(toset~({\uniddcgcg} X1 : \iota .  m2\_finseq\_2~X1~k1\_numbers~(k1\_euclid~X0)))~\\
({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~\\
X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  True)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  \\
k2\_euclid\_4~X0~X1~X2))\end{array}
\label{hyp:egedpffgfhdgmgjgegmgah}
\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}((r4\_euclidlp~X0~X1~X2){\unicdbdjded}((X1{\unicdcdgdad}k5\_euclid~X0){\unicdcdcdhd}(\\
(X2{\unicdcdgdad}k5\_euclid~X0){\unicdcdcdhd}(r1\_rvsum\_1~X1~X2))))))\end{array}
\label{hyp:egddpffgfhdgmgjgegmgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_euclid~X0))){\unicdbdjdcd}((v1\_euclid\_4~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}((X2{\unicdcdgdad}X3){\unicdcdcdhd}(X1=k2\_euclid\_4~X0~X2~X3))))))\end{array}
\label{hyp:egcdpffgfhdgmgjgegpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehgdhdpffgfhdgmgjgegmgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k1\_euclidlp~X0)){\unicdbdjdcd}\\
((r6\_euclidlp~X0~X1~X2){\unicdbdjdcd}((v1\_euclid\_4~X1~X0){\unicdcdcdhd}(v1\_euclid\_4~X2~X0)))))\end{array}$$
\end{theorem}
\end{document}
