\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}
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\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{t76\_matrix10 (TMHbohqpmLiU2P3M9ndM7aCp5t6bFMgoUsv)}
\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 $ v4\_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 $ v3\_matrix10 : {{\iota}{\unicdbdjdcd}{o}}$ 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}((v3\_matrix10~\\
X1){\unicdbdjdcd}(r2\_matrix10~(k3\_matrix10~X0~X1~X2)~X2))))\end{array}
\label{hyp:ehgdjdpfngbgehchjgihbdad}
\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}((v4\_matrix10~\\
X1){\unicdbdjdcd}(r2\_matrix10~X2~(k3\_matrix10~X0~X1~X2)))))\end{array}
\label{hyp:ehgdidpfngbgehchjgihbdad}
\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}({\unicdcdadad} X4 .  (m1\_matrix\_1~X4~\\
k1\_numbers~X0~X0){\unicdbdjdcd}((r2\_matrix10~(k3\_matrix10~X0~X1~X2)~(k3\_matrix10~\\
X0~X3~X4)){\unicdbdjdcd}(r2\_matrix10~(k4\_matrix10~X0~X1~X3)~(k4\_matrix10~X0~X4~\\
X2)))))))\end{array}
\label{hyp:ehgdadpfngbgehchjgihbdad}
\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}({\unicdcdadad} X4 .  (m1\_matrix\_1~X4~\\
k1\_numbers~X0~X0){\unicdbdjdcd}((r2\_matrix10~(k4\_matrix10~X0~X1~X2)~(k4\_matrix10~\\
X0~X3~X4)){\unicdbdjdcd}(r2\_matrix10~(k4\_matrix10~X0~X4~X3)~(k4\_matrix10~X0~X2~\\
X1)))))))\end{array}
\label{hyp:ehfdidpfngbgehchjgihbdad}
\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}({\unicdcdadad} X4 .  (m1\_matrix\_1~X4~\\
k1\_numbers~X0~X0){\unicdbdjdcd}((r2\_matrix10~(k4\_matrix10~X0~X1~X2)~(k4\_matrix10~\\
X0~X3~X4)){\unicdbdjdcd}(r2\_matrix10~(k4\_matrix10~X0~X4~X2)~(k4\_matrix10~X0~X3~\\
X1)))))))\end{array}
\label{hyp:ehfdhdpfngbgehchjgihbdad}
\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}({\unicdcdadad} X4 .  (m1\_matrix\_1~X4~\\
k1\_numbers~X0~X0){\unicdbdjdcd}((r2\_matrix10~(k4\_matrix10~X0~X1~X2)~(k4\_matrix10~\\
X0~X3~X4)){\unicdbdjdcd}(r2\_matrix10~(k4\_matrix10~X0~X1~X3)~(k4\_matrix10~X0~X2~\\
X4)))))))\end{array}
\label{hyp:ehfdgdpfngbgehchjgihbdad}
\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~(k4\_matrix10~\\
X0~X1~X2)~X3){\unicdbdjdcd}(r2\_matrix10~(k4\_matrix10~X0~X1~X3)~X2)))))\end{array}
\label{hyp:ehfdddpfngbgehchjgihbdad}
\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~X1~(k4\_matrix10~\\
X0~X2~X3)){\unicdbdjdcd}(r2\_matrix10~X3~(k4\_matrix10~X0~X2~X1))))))\end{array}
\label{hyp:ehfdcdpfngbgehchjgihbdad}
\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~(k4\_matrix10~\\
X0~X1~X2)~(k4\_matrix10~X0~X3~X2)){\unicdbdjdcd}(r2\_matrix10~X1~X3)))))\end{array}
\label{hyp:ehfdbdpfngbgehchjgihbdad}
\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}((r2\_matrix10~\\
X1~X2){\unicdbdjdcd}(v3\_matrix10~(k4\_matrix10~X0~X1~X2)))))\end{array}
\label{hyp:ehcdidpfngbgehchjgihbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdcdcdhd}(m1\_matrix\_1~X2~k1\_numbers~X0~X0))){\unicdbdjdcd}(m1\_matrix\_1~\\
(k4\_matrix10~X0~X1~X2)~k1\_numbers~X0~X0)\end{array}
\label{hyp:egehpflgedpfngbgehchjgihbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdcdcdhd}(m1\_matrix\_1~X2~k1\_numbers~X0~X0))){\unicdbdjdcd}(m1\_matrix\_1~\\
(k3\_matrix10~X0~X1~X2)~k1\_numbers~X0~X0)\end{array}
\label{hyp:egehpflgddpfngbgehchjgihbdad}
\end{equation}
\begin{theorem}\label{thm:ehhdgdpfngbgehchjgihbdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~X1~k1\_numbers~\\
X0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~k1\_numbers~X0~X0){\unicdbdjdcd}((v4\_matrix10~\\
X1){\unicdbdjdcd}(r2\_matrix10~(k4\_matrix10~X0~X2~X1)~X2))))\end{array}$$
\end{theorem}
\end{document}
