\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{t47\_quaterni (TMSXP5XJt3DYtbQrc98GRcMW5ybYEzFmiBg)}
\maketitle
Let $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_quaterni : {\iota}$ be given.
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\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 $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k31\_quaterni~X0=k6\_quaterni~(k17\_quaterni~\\
X0)~(k1\_real\_1~(k18\_quaterni~X0))~(k1\_real\_1~(k19\_quaterni~X0))~\\
(k1\_real\_1~(k20\_quaterni~X0)))\end{array}
\label{hyp:ehedddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k17\_quaterni~k22\_quaterni=np\_\_1){\unicdcdcdhd}((k18\_quaterni~k22\_quaterni=\\
k6\_numbers){\unicdcdcdhd}((k19\_quaterni~k22\_quaterni=k6\_numbers){\unicdcdcdhd}(k20\_quaterni~\\
k22\_quaterni=k6\_numbers)))\end{array}
\label{hyp:ehcdjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{{{{{k6\_quaterni}~{np\_\_1}}~{k6\_numbers}}~{k6\_numbers}}~{k6\_numbers}}={np\_\_1}}\label{hyp:mgfdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={{k1\_real\_1}~{k6\_numbers}}}\label{hyp:mgcdpfngfgdhggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k22\_quaterni}}\label{hyp:egehpflgcdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k22\_quaterni}={np\_\_1}}\label{hyp:egbdidpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfbhfhbgehfgchogjg}
${{{k31\_quaterni}~{k22\_quaterni}}={k22\_quaterni}}$.
\end{theorem}
\end{document}
