\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t15\_euclid\_7 (TMVumbJ689jyRsx9d5oDVq8zg84xWDAqihP)}
\maketitle
Let $ v1\_euclid\_7 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k23\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_euclid\_7~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finseq\_1~X1){\unicdcdcdhd}(v3\_valued\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finseq\_1~X2){\unicdcdcdhd}(v3\_valued\_0~\\
X2)))){\unicdbdjdcd}(((X1 \in X0){\unicdcdcdhd}(X2 \in X0)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(k23\_rvsum\_1~X1~X2=k6\_numbers)))))\end{array}
\label{hyp:egddpffgfhdgmgjgegpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v3\_valued\_0~\\
X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v3\_valued\_0~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))){\unicdbdjdcd}((r1\_rvsum\_1~X0~X1){\unicdbdjded}\\
(k23\_rvsum\_1~X0~X1=k6\_numbers)))\end{array}
\label{hyp:egbdhdpfchghdhfhngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpffgfhdgmgjgegpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_euclid\_7~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finseq\_1~X1){\unicdcdcdhd}(v3\_valued\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finseq\_1~X2){\unicdcdcdhd}(v3\_valued\_0~\\
X2)))){\unicdbdjdcd}(((X1 \in X0){\unicdcdcdhd}(X2 \in X0)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(r1\_rvsum\_1~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
