\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t13\_euclid\_7 (TMQrkaDthETgZcSBEPcRh7FFqRxrR7xL6fT)}
\maketitle
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_rfinseq2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_classes1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseq\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_integra2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((r2\_classes1~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdcdcdhd}((k9\_xtuple\_0~X2=k9\_xtuple\_0~\\
X0){\unicdcdcdhd}((k10\_xtuple\_0~X2=k9\_xtuple\_0~X1){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}(X0=\\
k3\_relat\_1~X2~X1)))))))\end{array}
\label{hyp:ehhdhdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_relat\_1~X1)){\unicdbdjdcd}((r2\_classes1~\\
X0~X1){\unicdbdjdcd}(r2\_classes1~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchcdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_funct\_1~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v2\_funct\_1~X1)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k3\_relat\_1~X0~X1)){\unicdcdcdhd}(v2\_funct\_1~(k3\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdghdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((v1\_integra2~(k6\_rfinseq2~\\
X0)){\unicdcdcdhd}(m2\_finseq\_1~(k6\_rfinseq2~X0)~k1\_numbers))\end{array}
\label{hyp:egehpflggdpfchggjgogdhfgbhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_integra2~\\
X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k1\_numbers)){\unicdbdjdcd}((X1=k6\_rfinseq2~X0){\unicdbdjded}(r2\_classes1~\\
X0~X1)))\end{array}
\label{hyp:eggdpfchggjgogdhfgbhcd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpffgfhdgmgjgegpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((v2\_funct\_1~X0){\unicdbdjded}(v2\_funct\_1~\\
(k6\_rfinseq2~X0)))\end{array}$$
\end{theorem}
\end{document}
