\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{t22\_matrix\_2 (TMMbEG9BRAxfnLmpampY7TpM9qjsgLjYp3G)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ 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 $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_matrix\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}\\
((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))))){\unicdbdjdcd}((r2\_relset\_1~X0~X0~(k1\_partfun1~X0~X0~X0~X0~X1~(k2\_funct\_2~\\
X0~X1))~(k6\_partfun1~X0)){\unicdcdcdhd}(r2\_relset\_1~X0~X0~(k1\_partfun1~X0~X0~\\
X0~X0~(k2\_funct\_2~X0~X1)~X1)~(k6\_partfun1~X0)))\end{array}
\label{hyp:ehgdbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_funct\_1~(k1\_finseq\_2~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k1\_finseq\_2~X0)~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0)){\unicdcdcdhd}\\
((v3\_funct\_2~(k1\_finseq\_2~X0)~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k1\_finseq\_2~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
X0)~(k2\_finseq\_1~X0)))))))\end{array}
\label{hyp:ehfdfdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k11\_matrix\_2}~{({{k12\_matrix\_2}~{X0}})}}={X0}})}}}\label{hyp:ehbdidpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}\\
((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))))){\unicdbdjdcd}(k2\_funct\_2~X0~X1=k2\_funct\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}(k1\_partfun1~X0~X1~X2~X3~X4~X5=k3\_relat\_1~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k12\_matrix\_2~X0)){\unicdcdcdhd}\\
(v3\_matrix\_2~(k12\_matrix\_2~X0)))\end{array}
\label{hyp:ggdgcdpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_matrix\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_matrix\_2~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_finseq\_1~\\
(k11\_matrix\_2~X0))~(k2\_finseq\_1~(k11\_matrix\_2~X0))){\unicdcdcdhd}((v3\_funct\_2~\\
X1~(k2\_finseq\_1~(k11\_matrix\_2~X0))~(k2\_finseq\_1~(k11\_matrix\_2~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
(k11\_matrix\_2~X0))~(k2\_finseq\_1~(k11\_matrix\_2~X0)))))))))\end{array}
\label{hyp:egehpfngbdpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~X0){\unicdcdcdhd}\\
((v3\_funct\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))))){\unicdbdjdcd}((v1\_funct\_1~(k2\_funct\_2~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k2\_funct\_2~\\
X0~X1)~X0~X0){\unicdcdcdhd}((v3\_funct\_2~(k2\_funct\_2~X0~X1)~X0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
(k2\_funct\_2~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0))))))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_partfun1~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_partfun1~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X3))))\end{array}
\label{hyp:egehpflgbdpfahbgchehggfhogbd}
\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}
\begin{theorem}\label{thm:ehcdcdpfngbgehchjgihpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_2~X1~(k12\_matrix\_2~\\
X0)){\unicdbdjdcd}((k1\_partfun1~(k2\_finseq\_1~(k11\_matrix\_2~(k12\_matrix\_2~\\
X0)))~(k2\_finseq\_1~(k11\_matrix\_2~(k12\_matrix\_2~X0)))~(k2\_finseq\_1~\\
(k11\_matrix\_2~(k12\_matrix\_2~X0)))~(k2\_finseq\_1~(k11\_matrix\_2~\\
(k12\_matrix\_2~X0)))~(k2\_funct\_2~(k2\_finseq\_1~(k11\_matrix\_2~(\\
k12\_matrix\_2~X0)))~X1)~X1=k1\_finseq\_2~X0){\unicdcdcdhd}(k1\_partfun1~(k2\_finseq\_1~\\
(k11\_matrix\_2~(k12\_matrix\_2~X0)))~(k2\_finseq\_1~(k11\_matrix\_2~\\
(k12\_matrix\_2~X0)))~(k2\_finseq\_1~(k11\_matrix\_2~(k12\_matrix\_2~\\
X0)))~(k2\_finseq\_1~(k11\_matrix\_2~(k12\_matrix\_2~X0)))~X1~(k2\_funct\_2~\\
(k2\_finseq\_1~(k11\_matrix\_2~(k12\_matrix\_2~X0)))~X1)=k1\_finseq\_2~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
