\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{l128\_quaterni (TMKaC4mdeV9TD6ojcUtzVAzBCpL2abKxz2M)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_xcmplx\_0~X0~X2)~(\\
k2\_xcmplx\_0~X1~X3))))))\end{array}
\label{hyp:mggdpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgfdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdcdidpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (v1\_xreal\_0~X6){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (v1\_xreal\_0~X7){\unicdbdjdcd}({\unicdcdadad} X8 .  (v1\_xreal\_0~X8){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(v1\_xreal\_0~X9){\unicdbdjdcd}({\unicdcdadad} X10 .  (v1\_xreal\_0~X10){\unicdbdjdcd}({\unicdcdadad} X11 .  \\
(v1\_xreal\_0~X11){\unicdbdjdcd}(((r1\_xxreal\_0~X6~X0){\unicdcdcdhd}((r1\_xxreal\_0~X7~X1){\unicdcdcdhd}\\
((r1\_xxreal\_0~X8~X2){\unicdcdcdhd}((r1\_xxreal\_0~X9~X3){\unicdcdcdhd}((r1\_xxreal\_0~X10~X4){\unicdcdcdhd}\\
(r1\_xxreal\_0~X11~X5)))))){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~X6~X7)~X8)~X9)~X10)~X11)~\\
(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~(k2\_xcmplx\_0~\\
X0~X1)~X2)~X3)~X4)~X5))))))))))))))\end{array}$$
\end{theorem}
\end{document}
