\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{t32\_quaterni (TMaEhABM9r31pUWebHSpDmkuF6xuKAw7HEe)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_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.
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}({\unicdcdadad} X3 .  (v1\_quaterni~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
v1\_quaterni~X4){\unicdbdjdcd}((X4=k7\_quaterni~(k7\_quaterni~(k7\_quaterni~\\
X0~X1)~X2)~X3){\unicdbdjdcd}((k17\_quaterni~X4=k7\_real\_1~(k7\_real\_1~(k7\_real\_1~\\
(k17\_quaterni~X0)~(k17\_quaterni~X1))~(k17\_quaterni~X2))~(k17\_quaterni~\\
X3)){\unicdcdcdhd}((k18\_quaterni~X4=k7\_real\_1~(k7\_real\_1~(k7\_real\_1~(k18\_quaterni~\\
X0)~(k18\_quaterni~X1))~(k18\_quaterni~X2))~(k18\_quaterni~X3)){\unicdcdcdhd}\\
((k19\_quaterni~X4=k7\_real\_1~(k7\_real\_1~(k7\_real\_1~(k19\_quaterni~\\
X0)~(k19\_quaterni~X1))~(k19\_quaterni~X2))~(k19\_quaterni~X3)){\unicdcdcdhd}\\
(k20\_quaterni~X4=k7\_real\_1~(k7\_real\_1~(k7\_real\_1~(k20\_quaterni~\\
X0)~(k20\_quaterni~X1))~(k20\_quaterni~X2))~(k20\_quaterni~X3))))))))))\end{array}
\label{hyp:mggdbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
v1\_quaterni~(k7\_quaterni~X0~X1))\end{array}
\label{hyp:ggdggdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_quaterni~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_quaterni~X3){\unicdbdjdcd}((k17\_quaterni~\\
(k7\_quaterni~(k7\_quaterni~(k7\_quaterni~X0~X1)~X2)~X3)=k7\_real\_1~\\
(k7\_real\_1~(k7\_real\_1~(k17\_quaterni~X0)~(k17\_quaterni~X1))~(k17\_quaterni~\\
X2))~(k17\_quaterni~X3)){\unicdcdcdhd}((k18\_quaterni~(k7\_quaterni~(k7\_quaterni~\\
(k7\_quaterni~X0~X1)~X2)~X3)=k7\_real\_1~(k7\_real\_1~(k7\_real\_1~(k18\_quaterni~\\
X0)~(k18\_quaterni~X1))~(k18\_quaterni~X2))~(k18\_quaterni~X3)){\unicdcdcdhd}\\
((k19\_quaterni~(k7\_quaterni~(k7\_quaterni~(k7\_quaterni~X0~X1)~\\
X2)~X3)=k7\_real\_1~(k7\_real\_1~(k7\_real\_1~(k19\_quaterni~X0)~(k19\_quaterni~\\
X1))~(k19\_quaterni~X2))~(k19\_quaterni~X3)){\unicdcdcdhd}(k20\_quaterni~(k7\_quaterni~\\
(k7\_quaterni~(k7\_quaterni~X0~X1)~X2)~X3)=k7\_real\_1~(k7\_real\_1~\\
(k7\_real\_1~(k20\_quaterni~X0)~(k20\_quaterni~X1))~(k20\_quaterni~\\
X2))~(k20\_quaterni~X3))))))))\end{array}$$
\end{theorem}
\end{document}
