\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{t46\_matrixj1 (TMLpmnpZ2ZA2iaLFTVCgtDPoRGUbEErpUiw)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\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 $ k10\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_matrixj1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_matrix\_1~X2~X1~X0~X0){\unicdbdjdcd}((k3\_finseq\_1~X2=X0){\unicdcdcdhd}((k1\_matrix\_1~\\
X2=X0){\unicdcdcdhd}(k2\_matrix\_1~X2=k2\_zfmisc\_1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~\\
X0))))))\end{array}
\label{hyp:ehcdedpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\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 .  {\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))))){\unicdbdjdcd}(k2\_matrixj1~\\
X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_matrixj1~\\
X1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0))))){\unicdbdjdcd}(k14\_matrixj1~\\
X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdedpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_matrixj1~X1~X0){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0))))){\unicdbdjdcd}(k11\_matrixj1~\\
X0~X1=k9\_matrixj1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_matrixj1~X1~X0){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0))))){\unicdbdjdcd}(k10\_matrixj1~\\
X0~X1=k8\_matrixj1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_finset\_1}~{k4\_ordinal1}}}}\label{hyp:ggdghdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_matrixj1~X1~X0){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0))))){\unicdbdjdcd}(m2\_finseq\_1~\\
(k9\_matrixj1~X0~X1)~k5\_numbers)\end{array}
\label{hyp:egehpflgjdpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(m2\_subset\_1~(k3\_finseq\_1~X0)~k1\_numbers~k5\_numbers)\end{array}
\label{hyp:egehpflgddpfggjgogdhfgbhpfbd}
\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))))){\unicdbdjdcd}((v1\_matrix\_1~\\
(k2\_matrixj1~X0~X1~X2)){\unicdcdcdhd}(m2\_finseq\_1~(k2\_matrixj1~X0~X1~X2)~(k3\_finseq\_2~\\
X0)))\end{array}
\label{hyp:egehpflgcdpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_matrixj1~\\
X1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0))))){\unicdbdjdcd}(m1\_matrix\_1~\\
(k14\_matrixj1~X0~X1~X2)~X0~(k3\_finseq\_1~(k2\_matrixj1~X0~X1~X2))~(\\
k3\_finseq\_1~(k2\_matrixj1~X0~X1~X2)))\end{array}
\label{hyp:egehpflgbdedpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrixj1~X1~X0){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}((X2=k9\_matrixj1~X0~X1){\unicdbdjded}((k4\_finseq\_1~\\
X2=k4\_finseq\_1~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((X3 \in k4\_finseq\_1~\\
X2){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k1\_matrix\_1~(k2\_matrixj1~X0~X1~X3))))))))\end{array}
\label{hyp:egedpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrixj1~X1~X0){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}((X2=k8\_matrixj1~X0~X1){\unicdbdjded}((k4\_finseq\_1~\\
X2=k4\_finseq\_1~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((X3 \in k4\_finseq\_1~\\
X2){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k3\_finseq\_1~(k2\_matrixj1~X0~X1~X3))))))))\end{array}
\label{hyp:egddpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_finset\_1~X1))\end{array}
\label{hyp:dgdgcdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_finseq\_1~X1~(k3\_finseq\_2~\\
(k3\_finseq\_2~X0))){\unicdbdjdcd}((v2\_matrixj1~X1~X0){\unicdbdjdcd}(v1\_matrixj1~X1~X0)))\end{array}
\label{hyp:dgdgbdpfngbgehchjgihkgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X0}})}}}\label{hyp:dgdgbdpfggjgogdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfngbgehchjgihkgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_matrixj1~X1~X0){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~(k3\_finseq\_2~X0)))){\unicdbdjdcd}(k10\_matrixj1~\\
X0~X1=k11\_matrixj1~X0~X1))\end{array}$$
\end{theorem}
\end{document}
