\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{t88\_matrixr2 (TMJTL98rfW6EfUPnJtueFD9b663wgen6q1h)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_matrixr2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_matrixr1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k13\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~\\
(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}(((X0=k1\_matrix\_1~X2){\unicdbdjdcd}(k6\_matrixr1~\\
X2~(k4\_matrixr2~X0)=X2)){\unicdcdcdhd}((X1=k3\_finseq\_1~X2){\unicdbdjdcd}(k6\_matrixr1~\\
(k4\_matrixr2~X1)~X2=X2)))))\end{array}
\label{hyp:ehgdjdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~\\
X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}((X1=k10\_matrixr1~\\
X0){\unicdbdjded}((k8\_matrix\_1~k1\_numbers~X1~np\_\_1=X0){\unicdcdcdhd}(k3\_finseq\_1~X1=np\_\_1))))\end{array}
\label{hyp:ehedidpfngbgehchjgihchbd}
\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}
{{\unicdcdadad} X0 .  {{{k3\_finseq\_2}~{X0}}={{k13\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\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 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(m1\_matrix\_1~(k4\_matrixr2~\\
X0)~k1\_numbers~X0~X0)\end{array}
\label{hyp:egehpflgedpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((v1\_matrix\_1~(k10\_matrixr1~\\
X0)){\unicdcdcdhd}(m2\_finseq\_1~(k10\_matrixr1~X0)~(k3\_finseq\_2~k1\_numbers)))\end{array}
\label{hyp:egehpflgbdadpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k1\_numbers){\unicdbdjdcd}(k12\_matrixr1~X0~X1=\\
k8\_matrix\_1~k1\_numbers~(k6\_matrixr1~(k10\_matrixr1~X1)~X0)~np\_\_1))\end{array}
\label{hyp:egbdcdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~\\
X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}((X1=k10\_matrixr1~\\
X0){\unicdbdjded}((k1\_matrix\_1~X1=k3\_finseq\_1~X0){\unicdcdcdhd}((k3\_finseq\_1~X1=np\_\_1){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((X2 \in k4\_finseq\_1~X0){\unicdbdjdcd}(k3\_matrix\_1~\\
k1\_numbers~X1~np\_\_1~X2=k1\_seq\_1~X0~X2)))))))\end{array}
\label{hyp:egbdadpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehididpfngbgehchjgihchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k1\_numbers){\unicdbdjdcd}((k3\_finseq\_1~X1=X0){\unicdbdjdcd}(k12\_matrixr1~(k4\_matrixr2~\\
X0)~X1=X1)))\end{array}$$
\end{theorem}
\end{document}
