\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{t1\_quatern3 (TMdFbZFSGuk2QWH8fRF8ysAfMoqBpxazBVu)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k27\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\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\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}((\\
k17\_quaterni~(k27\_quaterni~X0~X1)=k9\_real\_1~(k9\_real\_1~(k9\_real\_1~\\
(k8\_real\_1~(k17\_quaterni~X0)~(k17\_quaterni~X1))~(k8\_real\_1~(k18\_quaterni~\\
X0)~(k18\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k19\_quaterni~\\
X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k20\_quaterni~X1))){\unicdcdcdhd}((k18\_quaterni~\\
(k27\_quaterni~X0~X1)=k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k18\_quaterni~X1))~(k8\_real\_1~(k18\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k20\_quaterni~\\
X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k19\_quaterni~X1))){\unicdcdcdhd}((k19\_quaterni~\\
(k27\_quaterni~X0~X1)=k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k19\_quaterni~X1))~(k8\_real\_1~(k19\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k18\_quaterni~\\
X1)))~(k8\_real\_1~(k18\_quaterni~X0)~(k20\_quaterni~X1))){\unicdcdcdhd}(k20\_quaterni~\\
(k27\_quaterni~X0~X1)=k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k20\_quaterni~X1))~(k8\_real\_1~(k20\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k18\_quaterni~X0)~(k19\_quaterni~\\
X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k18\_quaterni~X1)))))))\end{array}
\label{hyp:ehjdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k20\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdadpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k19\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k18\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k17\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k8\_real\_1~X0~X1=k8\_real\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}(k17\_quaterni~\\
(k27\_quaterni~X0~X1)=k17\_quaterni~(k27\_quaterni~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
