\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{t36\_quatern3 (TMJhJdhcBG6hmtKSkgv68QfjxFTKRbfsVvd)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_quatern2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k29\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k26\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k28\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k32\_quaterni~(k28\_quaterni~X0)=\\
k32\_quaterni~X0)\end{array}
\label{hyp:ehhdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_quaterni~X2){\unicdbdjdcd}(k26\_quaterni~(k29\_quaterni~X0~X1)~X2=k29\_quaterni~\\
(k26\_quaterni~X0~X2)~X1)))\end{array}
\label{hyp:ehgdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_quaterni~X2){\unicdbdjdcd}(r1\_xxreal\_0~(k3\_quatern2~(k26\_quaterni~(k26\_quaterni~\\
X0~X1)~X2))~(k7\_real\_1~(k7\_real\_1~(k3\_quatern2~X0)~(k3\_quatern2~\\
X1))~(k3\_quatern2~X2)))))\end{array}
\label{hyp:ehddfdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_quaterni~X2){\unicdbdjdcd}(k26\_quaterni~(k26\_quaterni~X0~X1)~X2=k26\_quaterni~\\
X0~(k26\_quaterni~X1~X2))))\end{array}
\label{hyp:ehcdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k3\_quatern2}~{X0}}={{k32\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
k29\_quaterni~X0~X1=k9\_quaterni~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k28\_quaterni}~{X0}}={{k8\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
k26\_quaterni~X0~X1=k7\_quaterni~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdgdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{v1\_quaterni}~{({{k8\_quaterni}~{X0}})}})}}}\label{hyp:egehpflgidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}(k9\_quaterni~\\
X0~X1=k7\_quaterni~X0~(k8\_quaterni~X1)))\end{array}
\label{hyp:egjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
k26\_quaterni~X0~X1=k26\_quaterni~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdgdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_quaterni~X2){\unicdbdjdcd}(r1\_xxreal\_0~(k3\_quatern2~(k29\_quaterni~(k26\_quaterni~\\
X0~X1)~X2))~(k7\_real\_1~(k7\_real\_1~(k3\_quatern2~X0)~(k3\_quatern2~\\
X1))~(k3\_quatern2~X2)))))\end{array}$$
\end{theorem}
\end{document}
