\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{t28\_matrix\_3 (TMVShpwmML9VqHX9YiGh3mYnivK8Cg1sytd)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r6\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k8\_matrix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_matrix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k10\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k9\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X0))))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k5\_finsub\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~\\
(k5\_finsub\_1~X2)){\unicdbdjdcd}(((v1\_setwiseo~X3~X0){\unicdcdcdhd}((v1\_binop\_1~X3~X0){\unicdcdcdhd}\\
((v2\_binop\_1~X3~X0){\unicdcdcdhd}((v1\_finseqop~X3~X0){\unicdcdcdhd}(r6\_binop\_1~X0~X4~X3))))){\unicdbdjdcd}\\
(k7\_setwiseo~(k2\_zfmisc\_1~X1~X2)~X0~X3~(k8\_matrix\_3~X1~X2~X7~X8)~(\\
k9\_matrix\_3~X1~X2~X0~X4~X5~X6)=k7\_setwiseo~X1~X0~X3~X7~(k9\_funcop\_1~\\
X0~X1~X4~X5~(k7\_setwiseo~X2~X0~X3~X8~X6))))))))))))\end{array}
\label{hyp:ehcdgdpfngbgehchjgihpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~\\
X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X1)~X1))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(\\
k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1)~X1))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
(((v1\_binop\_1~X4~X1){\unicdcdcdhd}((v2\_binop\_1~X4~X1){\unicdcdcdhd}((v1\_setwiseo~X4~X1){\unicdcdcdhd}\\
((v1\_finseqop~X4~X1){\unicdcdcdhd}(r6\_binop\_1~X1~X5~X4))))){\unicdbdjdcd}(k5\_binop\_1~X1~\\
X5~(k7\_setwiseo~X0~X1~X4~X2~X6)~X3=k7\_setwiseo~X0~X1~X4~X2~(k9\_funcop\_1~\\
X1~X0~X5~X6~X3)))))))))\end{array}
\label{hyp:ehbdfdpfdhfgehhhpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~\\
X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X1)~X1))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(\\
k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1)~X1))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
(((v1\_binop\_1~X4~X1){\unicdcdcdhd}((v2\_binop\_1~X4~X1){\unicdcdcdhd}((v1\_setwiseo~X4~X1){\unicdcdcdhd}\\
((v1\_finseqop~X4~X1){\unicdcdcdhd}(r6\_binop\_1~X1~X5~X4))))){\unicdbdjdcd}(k5\_binop\_1~X1~\\
X5~X3~(k7\_setwiseo~X0~X1~X4~X2~X6)=k7\_setwiseo~X0~X1~X4~X2~(k10\_funcop\_1~\\
X1~X0~X5~X3~X6)))))))))\end{array}
\label{hyp:ehbdedpfdhfgehhhpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~\\
X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X1)~X1))))){\unicdcdcdhd}((m1\_subset\_1~X3~(k5\_finsub\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))))))){\unicdbdjdcd}(m1\_subset\_1~(k7\_setwiseo~X0~X1~X2~X3~X4)~X1)\end{array}
\label{hyp:egehpflghdpfdhfgehhhjgdhfgpg}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfngbgehchjgihpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X0))))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k5\_finsub\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~\\
(k5\_finsub\_1~X2)){\unicdbdjdcd}(((v1\_setwiseo~X3~X0){\unicdcdcdhd}((v1\_binop\_1~X3~X0){\unicdcdcdhd}\\
((v2\_binop\_1~X3~X0){\unicdcdcdhd}((v1\_finseqop~X3~X0){\unicdcdcdhd}((r6\_binop\_1~X0~X4~X3){\unicdcdcdhd}\\
(v1\_binop\_1~X4~X0)))))){\unicdbdjdcd}(k7\_setwiseo~(k2\_zfmisc\_1~X1~X2)~X0~X3~\\
(k8\_matrix\_3~X1~X2~X7~X8)~(k9\_matrix\_3~X1~X2~X0~X4~X5~X6)=k7\_setwiseo~\\
X2~X0~X3~X8~(k10\_funcop\_1~X0~X2~X4~(k7\_setwiseo~X1~X0~X3~X7~X5)~X6)))))))))))\end{array}$$
\end{theorem}
\end{document}
