\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{t83\_matrixr2 (TMHAPZcPEmFf44M8dQPYiWRy3YbnXYBw3pi)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_matrixr2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_matrixr2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_matrixr2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_matrixr2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}(k1\_matrixr2~X0~X1~(k4\_matrixr2~X0)=X1))\end{array}
\label{hyp:ehhdbdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\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}(k1\_matrixr2~\\
X0~(k1\_matrixr2~X0~X1~X2)~X3=k1\_matrixr2~X0~X1~(k1\_matrixr2~X0~X2~\\
X3)))))\end{array}
\label{hyp:ehcdidpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0)){\unicdbdjdcd}(m1\_matrix\_1~(k7\_matrixr2~X0~X1)~k1\_numbers~\\
X0~X0)\end{array}
\label{hyp:egehpflghdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((m1\_matrix\_1~X1~k1\_numbers~X0~X0){\unicdcdcdhd}(m1\_matrix\_1~X2~k1\_numbers~\\
X0~X0))){\unicdbdjdcd}(m1\_matrix\_1~(k1\_matrixr2~X0~X1~X2)~k1\_numbers~X0~X0)\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}((v1\_matrixr2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~\\
X2~k1\_numbers~X0~X0){\unicdbdjdcd}((X2=k7\_matrixr2~X0~X1){\unicdbdjded}((k1\_matrixr2~X0~\\
X2~X1=k4\_matrixr2~X0){\unicdcdcdhd}(k1\_matrixr2~X0~X1~X2=k4\_matrixr2~X0))))))\end{array}
\label{hyp:eggdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}((v1\_matrixr2~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_matrix\_1~\\
X2~k1\_numbers~X0~X0){\unicdcdcdhd}((k1\_matrixr2~X0~X2~X1=k4\_matrixr2~X0){\unicdcdcdhd}(k1\_matrixr2~\\
X0~X1~X2=k4\_matrixr2~X0)))))\end{array}
\label{hyp:egfdpfngbgehchjgihchcd}
\end{equation}
\begin{theorem}\label{thm:ehidddpfngbgehchjgihchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~k1\_numbers~X0~\\
X0){\unicdbdjdcd}(((v1\_matrixr2~X1~X0){\unicdcdcdhd}(v1\_matrixr2~X2~X0)){\unicdbdjdcd}((v1\_matrixr2~\\
(k1\_matrixr2~X0~X1~X2)~X0){\unicdcdcdhd}(k7\_matrixr2~X0~(k1\_matrixr2~X0~X1~X2)=\\
k1\_matrixr2~X0~(k7\_matrixr2~X0~X2)~(k7\_matrixr2~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
