\documentclass{article}
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\begin{document}
\title{l2\_metric\_1 (TMVPPywYRpbeS2NqFoNWEsKxNjsCygtKFQk)}
\maketitle
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_funct\_5 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k13\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_funct\_5 : {\iota}$ be given.
Let $ k17\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k1\_binop\_1~(k13\_funcop\_1~X0~\\
X1~X2)~X0~X1=X2\end{array}
\label{hyp:ehhdbdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k9\_funct\_5}={k7\_funct\_5}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k17\_funcop\_1~X0~X1~X2=k13\_funcop\_1~\\
X0~X1~X2\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdhdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_funct\_5}={{{{k17\_funcop\_1}~{k1\_xboole\_0}}~{k1\_xboole\_0}}~{k1\_xboole\_0}}}\label{hyp:eggdpfggfhogdgehpffd}
\end{equation}
\begin{theorem}\label{thm:mgcdpfngfgehchjgdgpfbd}
${{{{{k1\_binop\_1}~{k9\_funct\_5}}~{k1\_xboole\_0}}~{k1\_xboole\_0}}={k6\_numbers}}$.
\end{theorem}
\end{document}
