\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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\begin{document}
\title{t65\_quaterni (TMcNSGrE59VwRpwLnMhzyPgFq5NRa6snVN7)}
\maketitle
Let $ k32\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_quaterni : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((X0=k6\_numbers){\unicdbdjdcd}(k7\_real\_1~(k7\_real\_1~\\
(k7\_real\_1~(k5\_square\_1~(k17\_quaterni~X0))~(k5\_square\_1~(k18\_quaterni~\\
X0)))~(k5\_square\_1~(k19\_quaterni~X0)))~(k5\_square\_1~(k20\_quaterni~\\
X0))=k6\_numbers))\end{array}
\label{hyp:ehcdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{{k7\_square\_1}~{k6\_numbers}}={k6\_numbers}}\label{hyp:ehbdhdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k21\_quaterni}}\label{hyp:egehpflgcdbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k32\_quaterni~X0=k7\_square\_1~(k7\_real\_1~\\
(k7\_real\_1~(k7\_real\_1~(k5\_square\_1~(k17\_quaterni~X0))~(k5\_square\_1~\\
(k18\_quaterni~X0)))~(k5\_square\_1~(k19\_quaterni~X0)))~(k5\_square\_1~\\
(k20\_quaterni~X0))))\end{array}
\label{hyp:egcdddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k21\_quaterni}={k6\_numbers}}\label{hyp:egbdhdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehgdfdpfbhfhbgehfgchogjg}
${{{k32\_quaterni}~{k21\_quaterni}}={k6\_numbers}}$.
\end{theorem}
\end{document}
