\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}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t30\_quaterni (TMd5FPGm6wBnh35jJe62q1TmnK29KTMTNoo)}
\maketitle
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xcmplx\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k7\_complex1 : {\iota}$ be given.
Let $ k5\_arytm\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_quaterni : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}((k17\_quaterni~(k6\_quaterni~X0~X1~\\
X2~X3)=X0){\unicdcdcdhd}((k18\_quaterni~(k6\_quaterni~X0~X1~X2~X3)=X1){\unicdcdcdhd}((k19\_quaterni~\\
(k6\_quaterni~X0~X1~X2~X3)=X2){\unicdcdcdhd}(k20\_quaterni~(k6\_quaterni~X0~X1~\\
X2~X3)=X3)))))))\end{array}
\label{hyp:ehcdddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_complex1}={k1\_xcmplx\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}(k6\_quaterni~X0~X1~k6\_numbers~k6\_numbers=k5\_arytm\_0~\\
X0~X1))\end{array}
\label{hyp:mgbdfdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xcmplx\_0}={{{k5\_arytm\_0}~{k6\_numbers}}~{np\_\_1}}}\label{hyp:mgbdddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k21\_quaterni}={k6\_numbers}}\label{hyp:egbdhdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehddadpfbhfhbgehfgchogjg}
$$\begin{array}{c}(k17\_quaterni~k1\_xcmplx\_0=k6\_numbers){\unicdcdcdhd}((k18\_quaterni~k1\_xcmplx\_0=\\
np\_\_1){\unicdcdcdhd}((k19\_quaterni~k1\_xcmplx\_0=k6\_numbers){\unicdcdcdhd}(k20\_quaterni~\\
k1\_xcmplx\_0=k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
