\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{t7\_quatern3 (TMUjBvwNhChKAtdaxPXkNKP5PodYR6a3ppo)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k27\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_quaterni : {\iota}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k26\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k23\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k25\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xcmplx\_0 : {\iota}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_quaterni : {\iota}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_quaterni : {\iota}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(X0=k26\_quaterni~(k26\_quaterni~\\
(k23\_quaterni~(k17\_quaterni~X0)~(k25\_quaterni~(k18\_quaterni~\\
X0)~k1\_xcmplx\_0))~(k25\_quaterni~(k19\_quaterni~X0)~k11\_quaterni))~\\
(k25\_quaterni~(k20\_quaterni~X0)~k12\_quaterni))\end{array}
\label{hyp:ehddhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((X0=X1){\unicdbdjdcd}((k17\_quaterni~(k10\_quaterni~X0~k12\_quaterni)=k6\_numbers){\unicdcdcdhd}\\
((k18\_quaterni~(k10\_quaterni~X0~k12\_quaterni)=k6\_numbers){\unicdcdcdhd}\\
((k19\_quaterni~(k10\_quaterni~X0~k12\_quaterni)=k6\_numbers){\unicdcdcdhd}\\
(k20\_quaterni~(k10\_quaterni~X0~k12\_quaterni)=X1))))))\end{array}
\label{hyp:ehddfdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
k27\_quaterni~X0~X1=k10\_quaterni~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k12\_quaterni}={k5\_quaterni}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}((\\
k17\_quaterni~(k10\_quaterni~X0~X1)=k9\_real\_1~(k9\_real\_1~(k9\_real\_1~\\
(k8\_real\_1~(k17\_quaterni~X0)~(k17\_quaterni~X1))~(k8\_real\_1~(k18\_quaterni~\\
X0)~(k18\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k19\_quaterni~\\
X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k20\_quaterni~X1))){\unicdcdcdhd}((k18\_quaterni~\\
(k10\_quaterni~X0~X1)=k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k18\_quaterni~X1))~(k8\_real\_1~(k18\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k20\_quaterni~\\
X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k19\_quaterni~X1))){\unicdcdcdhd}((k19\_quaterni~\\
(k10\_quaterni~X0~X1)=k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k19\_quaterni~X1))~(k8\_real\_1~(k19\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k18\_quaterni~\\
X1)))~(k8\_real\_1~(k18\_quaterni~X0)~(k20\_quaterni~X1))){\unicdcdcdhd}(k20\_quaterni~\\
(k10\_quaterni~X0~X1)=k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k20\_quaterni~X1))~(k8\_real\_1~(k20\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k18\_quaterni~X0)~(k19\_quaterni~\\
X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k18\_quaterni~X1)))))))\end{array}
\label{hyp:mggdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}(k10\_quaterni~\\
X0~X1=k6\_quaterni~(k9\_real\_1~(k9\_real\_1~(k9\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k17\_quaterni~X1))~(k8\_real\_1~(k18\_quaterni~\\
X0)~(k18\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k19\_quaterni~\\
X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k20\_quaterni~X1)))~(k9\_real\_1~\\
(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~(k17\_quaterni~X0)~(k18\_quaterni~\\
X1))~(k8\_real\_1~(k18\_quaterni~X0)~(k17\_quaterni~X1)))~(k8\_real\_1~\\
(k19\_quaterni~X0)~(k20\_quaterni~X1)))~(k8\_real\_1~(k20\_quaterni~\\
X0)~(k19\_quaterni~X1)))~(k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k19\_quaterni~X1))~(k8\_real\_1~(k19\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k18\_quaterni~\\
X1)))~(k8\_real\_1~(k18\_quaterni~X0)~(k20\_quaterni~X1)))~(k9\_real\_1~\\
(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~(k17\_quaterni~X0)~(k20\_quaterni~\\
X1))~(k8\_real\_1~(k20\_quaterni~X0)~(k17\_quaterni~X1)))~(k8\_real\_1~\\
(k18\_quaterni~X0)~(k19\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~\\
X0)~(k18\_quaterni~X1)))))\end{array}
\label{hyp:mggdgdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((\\
X0=k17\_quaterni~X0){\unicdcdcdhd}((k18\_quaterni~X0=k6\_numbers){\unicdcdcdhd}((k19\_quaterni~\\
X0=k6\_numbers){\unicdcdcdhd}(k20\_quaterni~X0=k6\_numbers)))))\end{array}
\label{hyp:mgcdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k5\_quaterni}}\label{hyp:ggdgfdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehhdpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k27\_quaterni~\\
X0~k12\_quaterni=k6\_quaterni~k6\_numbers~k6\_numbers~k6\_numbers~\\
(k17\_quaterni~X0)))\end{array}$$
\end{theorem}
\end{document}
