\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{t78\_quatern3 (TMZWXYELqYyQbLnAmwBz2QXpgeGXuE7N9vi)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_quatern3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_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 $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k27\_quaterni : {{\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~\\
X0)=k9\_real\_1~(k9\_real\_1~(k9\_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~X0)=k8\_real\_1~np\_\_2~(k8\_real\_1~(k17\_quaterni~X0)~(k18\_quaterni~\\
X0))){\unicdcdcdhd}((k19\_quaterni~(k27\_quaterni~X0~X0)=k8\_real\_1~np\_\_2~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k19\_quaterni~X0))){\unicdcdcdhd}(k20\_quaterni~(k27\_quaterni~\\
X0~X0)=k8\_real\_1~np\_\_2~(k8\_real\_1~(k17\_quaterni~X0)~(k20\_quaterni~\\
X0))))))\end{array}
\label{hyp:ehedadpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(X0=k6\_quaterni~(k17\_quaterni~X0)~\\
(k18\_quaterni~X0)~(k19\_quaterni~X0)~(k20\_quaterni~X0))\end{array}
\label{hyp:ehcdedpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{v1\_quaterni}~{({{k1\_quatern3}~{X0}})}})}}}\label{hyp:ggdgbdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k1\_quatern3}~{X0}}={{{k27\_quaterni}~{X0}}~{X0}}})}}}\label{hyp:egbdpfbhfhbgehfgchogdd}
\end{equation}
\begin{theorem}\label{thm:ehhdidpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k1\_quatern3~X0=k6\_quaterni~(k9\_real\_1~\\
(k9\_real\_1~(k9\_real\_1~(k5\_square\_1~(k17\_quaterni~X0))~(k5\_square\_1~\\
(k18\_quaterni~X0)))~(k5\_square\_1~(k19\_quaterni~X0)))~(k5\_square\_1~\\
(k20\_quaterni~X0)))~(k8\_real\_1~np\_\_2~(k8\_real\_1~(k17\_quaterni~\\
X0)~(k18\_quaterni~X0)))~(k8\_real\_1~np\_\_2~(k8\_real\_1~(k17\_quaterni~\\
X0)~(k19\_quaterni~X0)))~(k8\_real\_1~np\_\_2~(k8\_real\_1~(k17\_quaterni~\\
X0)~(k20\_quaterni~X0))))\end{array}$$
\end{theorem}
\end{document}
