\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{t11\_quaterni (TMZFxv5DGSffWiVQERgAkYcGCoDJjJV2Ssf)}
\maketitle
Let $ r2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (r2\_zfmisc\_1~X0~X1~X2~X3){\unicdbdjdcd}((k1\_funct\_1~(\\
k2\_quaterni~X0~X1~X2~X3~X4~X5~X6~X7)~X0=X4){\unicdcdcdhd}((k1\_funct\_1~(k2\_quaterni~\\
X0~X1~X2~X3~X4~X5~X6~X7)~X1=X5){\unicdcdcdhd}((k1\_funct\_1~(k2\_quaterni~X0~X1~X2~X3~\\
X4~X5~X6~X7)~X2=X6){\unicdcdcdhd}(k1\_funct\_1~(k2\_quaterni~X0~X1~X2~X3~X4~X5~X6~X7)~\\
X3=X7))))\end{array}
\label{hyp:ehddpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  {\unicdcdadad} X10 .  {\unicdcdadad} X11 .  \\
((r2\_zfmisc\_1~X0~X1~X2~X3){\unicdcdcdhd}(k2\_quaterni~X0~X1~X2~X3~X4~X5~X6~X7=k2\_quaterni~\\
X0~X1~X2~X3~X8~X9~X10~X11)){\unicdbdjdcd}((X4=X8){\unicdcdcdhd}((X5=X9){\unicdcdcdhd}((X6=X10){\unicdcdcdhd}(X7=X11))))\end{array}$$
\end{theorem}
\end{document}
