\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{t8\_matrix11 (TMF4LnbZCpWCe8Y6SfyycfDQ7kPQA7nUgZC)}
\maketitle
Let $ v7\_ordinal1 : {{\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\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}((v3\_xxreal\_0~X0){\unicdbdjded}(\preoh r1\_xxreal\_0~\\
k6\_numbers~X0))\end{array}
\label{hyp:eghdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
((X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((X2=k1\_funct\_1~X0~X1){\unicdbdjded}(k4\_tarski~X1~X2 \in \\
X0))){\unicdcdcdhd}((\preoh X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((X2=k1\_funct\_1~X0~X1){\unicdbdjded}(X2=k1\_xboole\_0))))\end{array}
\label{hyp:egcdpfggfhogdgehpfbd}
\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}((v4\_matrix\_2~\\
X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (v7\_ordinal1~X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (v7\_ordinal1~\\
X3){\unicdcdcdhd}((X2 \in k9\_xtuple\_0~X1){\unicdcdcdhd}((X3 \in k9\_xtuple\_0~X1){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}((\\
k1\_funct\_1~X1~X2=X3){\unicdcdcdhd}((k1\_funct\_1~X1~X3=X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}((X4 \in k9\_xtuple\_0~X1){\unicdbdjdcd}((X4=X2){\unicdcdcdid}((X4=X3){\unicdcdcdid}(k1\_funct\_1~X1~\\
X4=X4))))))))))))))\end{array}
\label{hyp:egbdbdpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{v7\_ordinal1}~{X0}})}{\unicdcdcdhd}{({\preoh{{{v3\_xxreal\_0}~{X0}}}})}})}}}\label{hyp:dgdgddpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidpfngbgehchjgihbdbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0)){\unicdcdcdhd}((v3\_funct\_2~\\
X1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~X0))))))){\unicdbdjdcd}((v4\_matrix\_2~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X3~X2){\unicdbdjdcd}((k1\_funct\_1~X1~X2=X3){\unicdbdjded}((X2 \in k9\_xtuple\_0~\\
X1){\unicdcdcdhd}((X3 \in k9\_xtuple\_0~X1){\unicdcdcdhd}((k1\_funct\_1~X1~X2=X3){\unicdcdcdhd}((k1\_funct\_1~\\
X1~X3=X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((X4 \in k9\_xtuple\_0~X1){\unicdbdjdcd}\\
((X4=X2){\unicdcdcdid}((X4=X3){\unicdcdcdid}(k1\_funct\_1~X1~X4=X4)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
