\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{t39\_matrixj1 (TMKFbJD2T9uMypBP2vheHzSowWmB4hqouTz)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_matrix13 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_wsierp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_matrixj1~X3~X0){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~\\
(k3\_finseq\_2~X0)))){\unicdbdjdcd}(X2=k6\_matrix13~X0~(k13\_matrixj1~X0~X1~(k3\_matrixj1~\\
X0~X3~(k4\_matrixj1~X0~X2)))~(k7\_subset\_1~k5\_numbers~(k2\_finseq\_1~\\
(k2\_nat\_1~(k3\_finseq\_1~X2)~(k2\_wsierp\_1~(k10\_matrixj1~X0~X3))))~\\
(k2\_finseq\_1~(k2\_wsierp\_1~(k10\_matrixj1~X0~X3))))~(k7\_subset\_1~\\
k5\_numbers~(k2\_finseq\_1~(k2\_nat\_1~(k1\_matrix\_1~X2)~(k2\_wsierp\_1~\\
(k11\_matrixj1~X0~X3))))~(k2\_finseq\_1~(k2\_wsierp\_1~(k11\_matrixj1~\\
X0~X3))))))))\end{array}
\label{hyp:ehddddpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_matrixj1~X3~X0){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~\\
(k3\_finseq\_2~X0)))){\unicdbdjdcd}(X2=k6\_matrix13~X0~(k13\_matrixj1~X0~X1~(k3\_matrixj1~\\
X0~(k4\_matrixj1~X0~X2)~X3))~(k2\_finseq\_1~(k3\_finseq\_1~X2))~(k2\_finseq\_1~\\
(k1\_matrix\_1~X2))))))\end{array}
\label{hyp:ehddcdpfngbgehchjgihkgbd}
\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}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_matrix\_1~\\
X1){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdcdcdhd}((v1\_matrix\_1~X2){\unicdcdcdhd}(m1\_finseq\_1~\\
X2~(k3\_finseq\_2~X0))))){\unicdbdjdcd}(k5\_matrixj1~X0~X1~X2=k10\_finseq\_1~X1~\\
X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~X0)))){\unicdbdjdcd}(k4\_matrixj1~X0~X1=k5\_finseq\_1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_matrixj1~\\
X1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0)))){\unicdcdcdhd}((v1\_matrixj1~\\
X2~X0){\unicdcdcdhd}(m1\_finseq\_1~X2~(k3\_finseq\_2~(k3\_finseq\_2~X0)))))){\unicdbdjdcd}(k3\_matrixj1~\\
X0~X1~X2=k7\_finseq\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~X0)))){\unicdbdjdcd}((v1\_matrixj1~(k4\_matrixj1~\\
X0~X1)~X0){\unicdcdcdhd}(m2\_finseq\_1~(k4\_matrixj1~X0~X1)~(k3\_finseq\_2~(k3\_finseq\_2~\\
X0))))\end{array}
\label{hyp:egehpflgedpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k10\_finseq\_1~X0~X1=k7\_finseq\_1~(k9\_finseq\_1~\\
X0)~(k9\_finseq\_1~X1)\end{array}
\label{hyp:egjdpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfngbgehchjgihkgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_matrix\_1~X3){\unicdcdcdhd}\\
(m2\_finseq\_1~X3~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_matrix\_1~\\
X4){\unicdcdcdhd}(m2\_finseq\_1~X4~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_matrix\_1~\\
X5){\unicdcdcdhd}(m2\_finseq\_1~X5~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_matrix\_1~\\
X6){\unicdcdcdhd}(m2\_finseq\_1~X6~(k3\_finseq\_2~X0))){\unicdbdjdcd}(((k3\_finseq\_1~X3=k3\_finseq\_1~\\
X5){\unicdcdcdhd}((k1\_matrix\_1~X3=k1\_matrix\_1~X5){\unicdcdcdhd}((k3\_finseq\_1~X4=k3\_finseq\_1~\\
X6){\unicdcdcdhd}((k1\_matrix\_1~X4=k1\_matrix\_1~X6){\unicdcdcdhd}(k13\_matrixj1~X0~X1~(k5\_matrixj1~\\
X0~X3~X4)=k13\_matrixj1~X0~X2~(k5\_matrixj1~X0~X5~X6)))))){\unicdbdjdcd}((X3=X5){\unicdcdcdhd}\\
(X4=X6)))))))))\end{array}$$
\end{theorem}
\end{document}
