\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{t49\_quaterni (TMM6CCDmZT6EURAfBWhvZosbM9v86ayWeT7)}
\maketitle
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_quaterni : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_quaterni : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_quaterni : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k31\_quaterni~X0)=\\
k17\_quaterni~X0){\unicdcdcdhd}((k18\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k18\_quaterni~X0)){\unicdcdcdhd}((k19\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k19\_quaterni~X0)){\unicdcdcdhd}(k20\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k20\_quaterni~X0)))))\end{array}
\label{hyp:ehededpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k17\_quaterni~k11\_quaterni=k6\_numbers){\unicdcdcdhd}((k18\_quaterni~k11\_quaterni=\\
k6\_numbers){\unicdcdcdhd}((k19\_quaterni~k11\_quaterni=np\_\_1){\unicdcdcdhd}((k20\_quaterni~\\
k11\_quaterni=k6\_numbers){\unicdcdcdhd}((k17\_quaterni~k12\_quaterni=k6\_numbers){\unicdcdcdhd}\\
((k18\_quaterni~k12\_quaterni=k6\_numbers){\unicdcdcdhd}((k19\_quaterni~k12\_quaterni=\\
k6\_numbers){\unicdcdcdhd}(k20\_quaterni~k12\_quaterni=np\_\_1)))))))\end{array}
\label{hyp:ehddbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={{k1\_real\_1}~{k6\_numbers}}}\label{hyp:mgcdpfngfgdhggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k11\_quaterni}}~{k1\_quaterni}}\label{hyp:egehpflgbdbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_quaterni}})}{\unicdbdjdcd}{({{v1\_quaterni}~{X0}})}}}\label{hyp:dgdgbdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehedjdpfbhfhbgehfgchogjg}
$$\begin{array}{c}(k17\_quaterni~(k31\_quaterni~k11\_quaterni)=k6\_numbers){\unicdcdcdhd}((k18\_quaterni~\\
(k31\_quaterni~k11\_quaterni)=k6\_numbers){\unicdcdcdhd}((k19\_quaterni~(k31\_quaterni~\\
k11\_quaterni)=k1\_real\_1~np\_\_1){\unicdcdcdhd}(k20\_quaterni~(k31\_quaterni~\\
k11\_quaterni)=k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
