\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{t60\_matrix13 (TMYS9zhPvjQ7QJYnoijakKcWUQYsntKEJw7)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_setfam\_1 : {{\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 $ k5\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_matrix13 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_matrix11 : {{\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 $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix13 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_matrix13 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_setfam\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k5\_numbers)))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (v7\_ordinal1~X1){\unicdcdcdhd}\\
(r1\_tarski~X0~(k2\_finseq\_1~X1)))\end{array}
\label{hyp:ehedddpfngbgehchjgihbddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_matrix\_1~X5~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m2\_finseq\_2~X6~k5\_numbers~(k4\_finseq\_2~X3~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m2\_finseq\_1~X7~X0){\unicdbdjdcd}({\unicdcdadad} X8 .  (v7\_ordinal1~X8){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m2\_finseq\_2~X9~k5\_numbers~(k4\_finseq\_2~X4~k5\_numbers)){\unicdbdjdcd}((r1\_tarski~\\
(k2\_zfmisc\_1~(k10\_xtuple\_0~X9)~(k10\_xtuple\_0~X6))~(k2\_matrix\_1~\\
X5)){\unicdbdjdcd}((X8 \in k10\_xtuple\_0~X9){\unicdcdcdid}(k1\_matrix13~X0~X5~X4~X3~X9~X6=k1\_matrix13~\\
X0~(k3\_matrix11~X8~X1~X2~X0~X5~X7)~X4~X3~X9~X6))))))))))))\end{array}
\label{hyp:ehddidpfngbgehchjgihbddd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\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 .  ((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_setfam\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k5\_numbers)))){\unicdbdjdcd}(k5\_matrix13~X0=k14\_finseq\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfngbgehchjgihbddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~X0~X1~X2){\unicdbdjdcd}\\
((v1\_matrix\_1~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~X0))))\end{array}
\label{hyp:egehpfngbdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_setfam\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k5\_numbers)))){\unicdbdjdcd}(m2\_finseq\_2~(k5\_matrix13~X0)~\\
k5\_numbers~(k4\_finseq\_2~(k5\_card\_1~X0)~k5\_numbers))\end{array}
\label{hyp:egehpflgfdpfngbgehchjgihbddd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{({{k5\_card\_1}~{X0}})}}~{k4\_ordinal1}})}}}\label{hyp:egehpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~X1){\unicdcdcdhd}((v7\_ordinal1~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X3){\unicdcdcdhd}((m1\_matrix\_1~X4~X3~X1~X2){\unicdcdcdhd}(m1\_finseq\_1~X5~X3)))))){\unicdbdjdcd}(m1\_matrix\_1~\\
(k3\_matrix11~X0~X1~X2~X3~X4~X5)~X3~X1~X2)\end{array}
\label{hyp:egehpflgddpfngbgehchjgihbdbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m2\_finseq\_1}~{({{k14\_finseq\_1}~{X0}})}}~{k5\_numbers}}}\label{hyp:egehpflgbdedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_finset\_1~\\
X2){\unicdcdcdhd}((v1\_setfam\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~k5\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_finset\_1~X3){\unicdcdcdhd}((v1\_setfam\_1~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~k5\_numbers)))){\unicdbdjdcd}(k6\_matrix13~X0~X1~X2~X3=k1\_matrix13~\\
X0~X1~(k5\_card\_1~X2)~(k5\_card\_1~X3)~(k5\_matrix13~X2)~(k5\_matrix13~\\
X3)))))\end{array}
\label{hyp:egcdpfngbgehchjgihbddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ({\unicdcdaddd} X1 .  (v7\_ordinal1~X1){\unicdcdcdhd}(r1\_tarski~X0~(k2\_finseq\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k5\_numbers){\unicdbdjdcd}((X1=k14\_finseq\_1~\\
X0){\unicdbdjded}((k10\_xtuple\_0~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
v7\_ordinal1~X5){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X3~X2){\unicdcdcdhd}\\
((r1\_xxreal\_0~X3~(k3\_finseq\_1~X1)){\unicdcdcdhd}((X4=k1\_funct\_1~X1~X2){\unicdcdcdhd}((\\
X5=k1\_funct\_1~X1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X5~X4)))))))))))))\end{array}
\label{hyp:egbdddpfggjgogdhfgbhpfbd}
\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:ehgdadpfngbgehchjgihbddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~X0~X1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_finset\_1~X4){\unicdcdcdhd}((v1\_setfam\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~k5\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_finseq\_1~X5~X0){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (v7\_ordinal1~X6){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_finset\_1~X7){\unicdcdcdhd}\\
((v1\_setfam\_1~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~k5\_numbers)))){\unicdbdjdcd}\\
((r1\_tarski~(k2\_zfmisc\_1~X7~X4)~(k2\_matrix\_1~X3)){\unicdbdjdcd}((X6 \in X7){\unicdcdcdid}(\\
k6\_matrix13~X0~X3~X7~X4=k6\_matrix13~X0~(k3\_matrix11~X6~X1~X2~X0~X3~\\
X5)~X7~X4))))))))))\end{array}$$
\end{theorem}
\end{document}
