\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{t82\_matrix10 (TMVqQXGakprtoPUt6z5Lq7MQ5LxNPZN8FAT)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v3\_matrix10 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_matrix10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_matrix10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_matrix10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~X1~k1\_numbers~\\
X0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~k1\_numbers~X0~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_matrix\_1~X3~k1\_numbers~X0~X0){\unicdbdjdcd}(((v3\_matrix10~X1){\unicdcdcdhd}(r2\_matrix10~\\
X2~X3)){\unicdbdjdcd}(r2\_matrix10~(k3\_matrix10~X0~X2~X1)~X3)))))\end{array}
\label{hyp:ehhdadpfngbgehchjgihbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~X1~k1\_numbers~\\
X0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~k1\_numbers~X0~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_matrix\_1~X3~k1\_numbers~X0~X0){\unicdbdjdcd}((r2\_matrix10~(k3\_matrix10~\\
X0~X1~X2)~X3){\unicdbdjdcd}(r2\_matrix10~X1~(k4\_matrix10~X0~X3~X2))))))\end{array}
\label{hyp:ehfdjdpfngbgehchjgihbdad}
\end{equation}
\begin{theorem}\label{thm:ehidcdpfngbgehchjgihbdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~X1~k1\_numbers~\\
X0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~k1\_numbers~X0~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_matrix\_1~X3~k1\_numbers~X0~X0){\unicdbdjdcd}(((v3\_matrix10~X1){\unicdcdcdhd}(r2\_matrix10~\\
X2~X3)){\unicdbdjdcd}(r2\_matrix10~X2~(k4\_matrix10~X0~X3~X1))))))\end{array}$$
\end{theorem}
\end{document}
