\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{t38\_matrix\_9 (TMd9BnSK9u5wSs7TNMDS3TcaqV1qAf7FQWS)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{{k1\_finseq\_2}~{np\_\_3}}={{{{k11\_finseq\_1}~{np\_\_1}}~{np\_\_2}}~{np\_\_3}}}\label{hyp:ehfdddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k2\_finseq\_1~np\_\_3)~\\
(k2\_finseq\_1~np\_\_3)){\unicdcdcdhd}((v3\_funct\_2~X0~(k2\_finseq\_1~np\_\_3)~(k2\_finseq\_1~\\
np\_\_3)){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
np\_\_3)~(k2\_finseq\_1~np\_\_3))))))){\unicdbdjdcd}(\preoh (X0=k3\_finseq\_4~k5\_numbers~\\
np\_\_2~np\_\_3~np\_\_1){\unicdcdcdhd}(v4\_matrix\_2~X0~np\_\_3))\end{array}
\label{hyp:ehddfdpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k2\_finseq\_1~np\_\_3)~\\
(k2\_finseq\_1~np\_\_3)){\unicdcdcdhd}((v3\_funct\_2~X0~(k2\_finseq\_1~np\_\_3)~(k2\_finseq\_1~\\
np\_\_3)){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
np\_\_3)~(k2\_finseq\_1~np\_\_3))))))){\unicdbdjdcd}(\preoh (X0=k3\_finseq\_4~k5\_numbers~\\
np\_\_3~np\_\_1~np\_\_2){\unicdcdcdhd}(v4\_matrix\_2~X0~np\_\_3))\end{array}
\label{hyp:ehddedpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0)){\unicdcdcdhd}((v3\_funct\_2~\\
X1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0))))))){\unicdbdjdcd}(\preoh (r2\_funct\_2~\\
(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0)~X1~(k6\_partfun1~(k2\_finseq\_1~\\
X0))){\unicdcdcdhd}(v4\_matrix\_2~X1~X0)))\end{array}
\label{hyp:ehddddpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k12\_matrix\_2~np\_\_3=k4\_enumset1~(k3\_finseq\_4~k5\_numbers~np\_\_1~\\
np\_\_2~np\_\_3)~(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1)~(k3\_finseq\_4~\\
k5\_numbers~np\_\_1~np\_\_3~np\_\_2)~(k3\_finseq\_4~k5\_numbers~np\_\_2~np\_\_3~\\
np\_\_1)~(k3\_finseq\_4~k5\_numbers~np\_\_2~np\_\_1~np\_\_3)~(k3\_finseq\_4~\\
k5\_numbers~np\_\_3~np\_\_1~np\_\_2)\end{array}
\label{hyp:ehbdjdpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X1~X0){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X0)))){\unicdbdjdcd}\\
(k3\_finseq\_4~X0~X1~X2~X3=k11\_finseq\_1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=k12\_matrix\_2~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_finseq\_1~\\
X0)~(k2\_finseq\_1~X0)){\unicdcdcdhd}((v3\_funct\_2~X2~(k2\_finseq\_1~X0)~(k2\_finseq\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
X0)~(k2\_finseq\_1~X0)))))))))\end{array}
\label{hyp:egjdpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k5\_finseq\_1}~{X0}}={{k1\_tarski}~{({{{k4\_tarski}~{np\_\_1}}~{X0}})}}}}\label{hyp:egfdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (X6=k4\_enumset1~X0~X1~X2~X3~X4~X5){\unicdbdjded}({\unicdcdadad} X7 .  (X7 \in X6){\unicdbdjded}\\
(\preoh (X7{\unicdcdgdad}X0){\unicdcdcdhd}((X7{\unicdcdgdad}X1){\unicdcdcdhd}((X7{\unicdcdgdad}X2){\unicdcdcdhd}((X7{\unicdcdgdad}X3){\unicdcdcdhd}((X7{\unicdcdgdad}X4){\unicdcdcdhd}(X7{\unicdcdgdad}X5)))))))\end{array}
\label{hyp:egedpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(k1\_finseq\_2~X0=k6\_partfun1~(k2\_finseq\_1~\\
X0))\end{array}
\label{hyp:egbdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k11\_finseq\_1~X0~X1~X2=k7\_finseq\_1~\\
(k7\_finseq\_1~(k9\_finseq\_1~X0)~(k9\_finseq\_1~X1))~(k9\_finseq\_1~\\
X2)\end{array}
\label{hyp:egbdadpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfngbgehchjgihpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k2\_finseq\_1~np\_\_3)~\\
(k2\_finseq\_1~np\_\_3)){\unicdcdcdhd}((v3\_funct\_2~X0~(k2\_finseq\_1~np\_\_3)~(k2\_finseq\_1~\\
np\_\_3)){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
np\_\_3)~(k2\_finseq\_1~np\_\_3))))))){\unicdbdjdcd}(\preoh (v4\_matrix\_2~X0~np\_\_3){\unicdcdcdhd}(\\
(X0{\unicdcdgdad}k3\_finseq\_4~k5\_numbers~np\_\_2~np\_\_1~np\_\_3){\unicdcdcdhd}((X0{\unicdcdgdad}k3\_finseq\_4~\\
k5\_numbers~np\_\_1~np\_\_3~np\_\_2){\unicdcdcdhd}(X0{\unicdcdgdad}k3\_finseq\_4~k5\_numbers~np\_\_3~\\
np\_\_2~np\_\_1))))\end{array}$$
\end{theorem}
\end{document}
