\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t11\_quatern3 (TMcoR2C4VqWiv7akh69nJb9ExVhsYQ6cWUa)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_quatern2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k27\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_quatern2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k27\_quaterni~X0~\\
(k31\_quaterni~X0))=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))){\unicdcdcdhd}((k18\_quaterni~\\
(k27\_quaterni~X0~(k31\_quaterni~X0))=k6\_numbers){\unicdcdcdhd}((k19\_quaterni~\\
(k27\_quaterni~X0~(k31\_quaterni~X0))=k6\_numbers){\unicdcdcdhd}(k20\_quaterni~\\
(k27\_quaterni~X0~(k31\_quaterni~X0))=k6\_numbers))))\end{array}
\label{hyp:ehgdadpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k18\_quatern2~X0~\\
X0)=k5\_square\_1~(k3\_quatern2~X0)){\unicdcdcdhd}((k18\_quaterni~(k18\_quatern2~\\
X0~X0)=k6\_numbers){\unicdcdcdhd}((k19\_quaterni~(k18\_quatern2~X0~X0)=k6\_numbers){\unicdcdcdhd}\\
(k19\_quaterni~(k18\_quatern2~X0~X0)=k6\_numbers))))\end{array}
\label{hyp:ehfdadpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}(k18\_quatern2~\\
X0~X1=k27\_quaterni~X0~(k31\_quaterni~X1)))\end{array}
\label{hyp:egbdbdpfbhfhbgehfgchogcd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k5\_square\_1~(k3\_quatern2~X0)=k7\_real\_1~\\
(k7\_real\_1~(k7\_real\_1~(k5\_square\_1~(k17\_quaterni~X0))~(k5\_square\_1~\\
(k18\_quaterni~X0)))~(k5\_square\_1~(k19\_quaterni~X0)))~(k5\_square\_1~\\
(k20\_quaterni~X0)))\end{array}$$
\end{theorem}
\end{document}
