\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{t42\_quaterni (TMPafgXAo8UpFEZRB9YtJGLGeMotCbgsFL7)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k29\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_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 $ k28\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\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 $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_xcmplx\_0 : {{\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.
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.
Let $ k16\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k17\_quaterni~X0)){\unicdcdcdhd}((k18\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k18\_quaterni~X0)){\unicdcdcdhd}((k19\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k19\_quaterni~X0)){\unicdcdcdhd}(k20\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k20\_quaterni~X0)))))\end{array}
\label{hyp:ehedbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}((\\
k17\_quaterni~(k26\_quaterni~X0~X1)=k7\_real\_1~(k17\_quaterni~X0)~\\
(k17\_quaterni~X1)){\unicdcdcdhd}((k18\_quaterni~(k26\_quaterni~X0~X1)=k7\_real\_1~\\
(k18\_quaterni~X0)~(k18\_quaterni~X1)){\unicdcdcdhd}((k19\_quaterni~(k26\_quaterni~\\
X0~X1)=k7\_real\_1~(k19\_quaterni~X0)~(k19\_quaterni~X1)){\unicdcdcdhd}(k20\_quaterni~\\
(k26\_quaterni~X0~X1)=k7\_real\_1~(k20\_quaterni~X0)~(k20\_quaterni~\\
X1))))))\end{array}
\label{hyp:ehddgdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k2\_xcmplx\_0~X0~(k4\_xcmplx\_0~X1)=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:dhahdgbdpfbgchjgehigng}
\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}(k9\_real\_1~X0~X1=k6\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfchfgbgmgpfbd}
\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}(k7\_real\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfchfgbgmgpfbd}
\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}{({{{k20\_quaterni}~{X0}}={{k16\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdadpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{{k1\_real\_1}~{X0}}={{k4\_xcmplx\_0}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k19\_quaterni}~{X0}}={{k15\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k18\_quaterni}~{X0}}={{k14\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k17\_quaterni}~{X0}}={{k13\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k14\_quaterni}~{X0}})}})}}}\label{hyp:ggdgjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k13\_quaterni}~{X0}})}})}}}\label{hyp:ggdgidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k16\_quaterni}~{X0}})}})}}}\label{hyp:ggdgbdbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k15\_quaterni}~{X0}})}})}}}\label{hyp:ggdgbdadpfbhfhbgehfgchogjg}
\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}(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 .  (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}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}((\\
k17\_quaterni~(k29\_quaterni~X0~X1)=k9\_real\_1~(k17\_quaterni~X0)~\\
(k17\_quaterni~X1)){\unicdcdcdhd}((k18\_quaterni~(k29\_quaterni~X0~X1)=k9\_real\_1~\\
(k18\_quaterni~X0)~(k18\_quaterni~X1)){\unicdcdcdhd}((k19\_quaterni~(k29\_quaterni~\\
X0~X1)=k9\_real\_1~(k19\_quaterni~X0)~(k19\_quaterni~X1)){\unicdcdcdhd}(k20\_quaterni~\\
(k29\_quaterni~X0~X1)=k9\_real\_1~(k20\_quaterni~X0)~(k20\_quaterni~\\
X1))))))\end{array}$$
\end{theorem}
\end{document}
