\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{t42\_matrix\_9 (TMUJz3E5qnn8hgrVdxvxBmWw23pwjCJRHaU)}
\maketitle
Let $ v1\_funct\_1 : {{\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\_\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ 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 $ v5\_matrix\_2 : {{\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 $ k12\_matrix\_2 : {{\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 $ k4\_ordinal1 : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_group\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k3\_finseq\_4~k5\_numbers~np\_\_1~np\_\_3~np\_\_2 \in k12\_matrix\_2~np\_\_3){\unicdcdcdhd}\\
((k3\_finseq\_4~k5\_numbers~np\_\_2~np\_\_3~np\_\_1 \in k12\_matrix\_2~np\_\_3){\unicdcdcdhd}\\
((k3\_finseq\_4~k5\_numbers~np\_\_2~np\_\_1~np\_\_3 \in k12\_matrix\_2~np\_\_3){\unicdcdcdhd}\\
((k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_1~np\_\_2 \in k12\_matrix\_2~np\_\_3){\unicdcdcdhd}\\
((k3\_finseq\_4~k5\_numbers~np\_\_1~np\_\_2~np\_\_3 \in k12\_matrix\_2~np\_\_3){\unicdcdcdhd}\\
(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1 \in k12\_matrix\_2~np\_\_3)))))\end{array}
\label{hyp:ehcdhdpfngbgehchjgihpfjd}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k13\_matrix\_2~np\_\_3))){\unicdbdjdcd}\\
(\preoh (k4\_nat\_d~(k3\_finseq\_1~X0)~np\_\_2=k6\_numbers){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}(\preoh (X1 \in k4\_finseq\_1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_matrix\_2~\\
X2~(k12\_matrix\_2~np\_\_3)){\unicdbdjdcd}(\preoh (k1\_funct\_1~X0~X1=X2){\unicdcdcdhd}(v4\_matrix\_2~\\
X2~(k11\_matrix\_2~(k12\_matrix\_2~np\_\_3))))))){\unicdcdcdhd}((k3\_group\_4~(k13\_matrix\_2~\\
np\_\_3)~X0{\unicdcdgdad}k3\_finseq\_4~k5\_numbers~np\_\_1~np\_\_2~np\_\_3){\unicdcdcdhd}((k3\_group\_4~\\
(k13\_matrix\_2~np\_\_3)~X0{\unicdcdgdad}k3\_finseq\_4~k5\_numbers~np\_\_2~np\_\_3~np\_\_1){\unicdcdcdhd}\\
(k3\_group\_4~(k13\_matrix\_2~np\_\_3)~X0{\unicdcdgdad}k3\_finseq\_4~k5\_numbers~np\_\_3~\\
np\_\_1~np\_\_2)))))\end{array}
\label{hyp:mggdadpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1{\unicdcdgdad}k3\_finseq\_4~k5\_numbers~\\
np\_\_2~np\_\_3~np\_\_1){\unicdcdcdhd}(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1{\unicdcdgdad}\\
k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_1~np\_\_2)\end{array}
\label{hyp:mgddgdpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k3\_finseq\_4~k5\_numbers~np\_\_1~np\_\_2~np\_\_3{\unicdcdgdad}k3\_finseq\_4~k5\_numbers~\\
np\_\_3~np\_\_2~np\_\_1\end{array}
\label{hyp:mgddcdpfngbgehchjgihpfjd}
\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}
\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}((v5\_matrix\_2~\\
X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_finseq\_1~X2~(u1\_struct\_0~(k13\_matrix\_2~\\
X0))){\unicdcdcdhd}((k4\_nat\_d~(k3\_finseq\_1~X2)~np\_\_2=k6\_numbers){\unicdcdcdhd}((X1=k3\_group\_4~\\
(k13\_matrix\_2~X0)~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\preoh (X3 \in k4\_finseq\_1~\\
X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_matrix\_2~X4~(k12\_matrix\_2~X0)){\unicdbdjdcd}(\preoh (k1\_funct\_1~\\
X2~X3=X4){\unicdcdcdhd}(v4\_matrix\_2~X4~(k11\_matrix\_2~(k12\_matrix\_2~X0))))))))))))\end{array}
\label{hyp:egbdcdpfngbgehchjgihpfcd}
\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:ehedcdpfngbgehchjgihpfjd}
$$\begin{array}{c}(v1\_funct\_1~(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1)~(k2\_finseq\_1~np\_\_3)~\\
(k2\_finseq\_1~np\_\_3)){\unicdcdcdhd}((v3\_funct\_2~(k3\_finseq\_4~k5\_numbers~np\_\_3~\\
np\_\_2~np\_\_1)~(k2\_finseq\_1~np\_\_3)~(k2\_finseq\_1~np\_\_3)){\unicdcdcdhd}((\preoh v5\_matrix\_2~\\
(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1)~np\_\_3){\unicdcdcdhd}(m1\_subset\_1~\\
(k3\_finseq\_4~k5\_numbers~np\_\_3~np\_\_2~np\_\_1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_finseq\_1~np\_\_3)~(k2\_finseq\_1~np\_\_3)))))))\end{array}$$
\end{theorem}
\end{document}
