\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{t26\_quatern2 (TMJG1rtq6zJxHBTmoDL7Mmbbkc5SMp3bzjz)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_quaterni : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k31\_quaterni~X0)=\\
k17\_quaterni~X0){\unicdcdcdhd}((k18\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k18\_quaterni~X0)){\unicdcdcdhd}((k19\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k19\_quaterni~X0)){\unicdcdcdhd}(k20\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k20\_quaterni~X0)))))\end{array}
\label{hyp:ehededpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}((\\
(k17\_quaterni~X0=k17\_quaterni~X1){\unicdcdcdhd}((k18\_quaterni~X0=k18\_quaterni~\\
X1){\unicdcdcdhd}((k19\_quaterni~X0=k19\_quaterni~X1){\unicdcdcdhd}(k20\_quaterni~X0=k20\_quaterni~\\
X1)))){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehcdfdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{{k1\_real\_1}~{({{k1\_real\_1}~{X0}})}}={X0}})}}}\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k31\_quaterni~X0)~k1\_quaterni)\end{array}
\label{hyp:egehpflgddbdpfbhfhbgehfgchogjg}
\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}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_quaterni}})}{\unicdbdjdcd}{({{v1\_quaterni}~{X0}})}}}\label{hyp:dgdgbdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfbhfhbgehfgchogcd}
${{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k31\_quaterni}~{({{k31\_quaterni}~{X0}})}}={X0}})}}}$.
\end{theorem}
\end{document}
