\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{t51\_euclid\_7 (TMUVpqVca6HwgYpmdgXQkZ8vFzZNGx4NFhg)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_rusub\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_rusub\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_euclid\_7 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_bhsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_bhsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_rusub\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_bhsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}(m1\_rusub\_3~\\
(k8\_euclid\_7~X0)~(k7\_real\_ns1~X0))\end{array}
\label{hyp:ehedjdpffgfhdgmgjgegpfhd}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~\\
k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finset\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v2\_finseq\_1~X0)))))))\end{array}
\label{hyp:chdgfdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_finset\_1~(k8\_euclid\_7~X0)){\unicdcdcdhd}\\
(k1\_card\_1~(k8\_euclid\_7~X0)=X0))\end{array}
\label{hyp:mgfdhdpffgfhdgmgjgegpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k7\_real\_ns1~X0)){\unicdcdcdhd}\\
((v13\_algstr\_0~(k7\_real\_ns1~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k7\_real\_ns1~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k7\_real\_ns1~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k7\_real\_ns1~\\
X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k7\_real\_ns1~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k7\_real\_ns1~\\
X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k7\_real\_ns1~X0)){\unicdcdcdhd}((v8\_rlvect\_1~(k7\_real\_ns1~\\
X0)){\unicdcdcdhd}((v1\_bhsp\_1~(k7\_real\_ns1~X0)){\unicdcdcdhd}(v2\_bhsp\_1~(k7\_real\_ns1~\\
X0))))))))))))\end{array}
\label{hyp:ggdggdpfchfgbgmgpfogdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}((\preoh v2\_struct\_0~(k7\_real\_ns1~\\
X0)){\unicdcdcdhd}((v1\_bhsp\_1~(k7\_real\_ns1~X0)){\unicdcdcdhd}(v1\_rusub\_4~(k7\_real\_ns1~\\
X0))))\end{array}
\label{hyp:ggdgbdfdpffgfhdgmgjgegpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k7\_real\_ns1~X0)){\unicdcdcdhd}\\
((v1\_bhsp\_1~(k7\_real\_ns1~X0)){\unicdcdcdhd}(l1\_bhsp\_1~(k7\_real\_ns1~X0))))\end{array}
\label{hyp:egehpflghdpfchfgbgmgpfogdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}((v2\_bhsp\_1~\\
X0){\unicdcdcdhd}(l1\_bhsp\_1~X0))))))))))){\unicdbdjdcd}(m1\_subset\_1~(k1\_rusub\_4~X0)~k5\_numbers)\end{array}
\label{hyp:egehpflgbdpfchfhdhfhcgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}((v2\_bhsp\_1~\\
X0){\unicdcdcdhd}(l1\_bhsp\_1~X0))))))))))){\unicdbdjdcd}((v1\_rusub\_4~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}((X1=k1\_rusub\_4~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_rusub\_3~X2~X0){\unicdbdjdcd}(X1=k1\_card\_1~X2)))))\end{array}
\label{hyp:egcdpfchfhdhfhcgpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0))))\end{array}
\label{hyp:dgdghdpfchfgmgbgehpfbd}
\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:ehfdbdpffgfhdgmgjgegpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k1\_rusub\_4~\\
(k7\_real\_ns1~X0)=X0)\end{array}$$
\end{theorem}
\end{document}
