\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{t66\_matrixr2 (TMQwtV8F5xCavwNj9rCjVf9sCZhCtEiKS63)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k7\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\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 $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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}((\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdbdjdcd}(k3\_matrixr1~(\\
k8\_matrixr1~X0~X1)~(k8\_matrixr1~X0~X1)=k8\_matrixr1~X0~X1)))\end{array}
\label{hyp:ehgdfdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}\\
(m2\_finseq\_1~X2~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}(((k3\_finseq\_1~X1=\\
k3\_finseq\_1~X2){\unicdcdcdhd}(k1\_matrix\_1~X1=k1\_matrix\_1~X2)){\unicdbdjdcd}(k7\_matrixr1~\\
X0~(k3\_matrixr1~X1~X2)=k3\_matrixr1~(k7\_matrixr1~X0~X1)~(k7\_matrixr1~\\
X0~X2)))))\end{array}
\label{hyp:ehedddpfngbgehchjgihchbd}
\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 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(((k3\_finseq\_1~X0=k3\_finseq\_1~X1){\unicdcdcdhd}((k1\_matrix\_1~X0=k1\_matrix\_1~\\
X1){\unicdcdcdhd}(X0=k3\_matrixr1~X0~X1))){\unicdbdjdcd}(X1=k8\_matrixr1~(k3\_finseq\_1~X0)~\\
(k1\_matrix\_1~X0))))\end{array}
\label{hyp:ehddhdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~\\
X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}((k3\_finseq\_1~\\
(k7\_matrixr1~X0~X1)=k3\_finseq\_1~X1){\unicdcdcdhd}(k1\_matrix\_1~(k7\_matrixr1~\\
X0~X1)=k1\_matrix\_1~X1)))\end{array}
\label{hyp:ehcdhdpfngbgehchjgihchbd}
\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}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
(v1\_matrix\_1~(k8\_matrixr1~X0~X1)){\unicdcdcdhd}(m2\_finseq\_1~(k8\_matrixr1~\\
X0~X1)~(k3\_finseq\_2~k1\_numbers)))\end{array}
\label{hyp:egehpflgidpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}(m1\_finseq\_1~\\
X1~(k3\_finseq\_2~k1\_numbers)))){\unicdbdjdcd}((v1\_matrix\_1~(k7\_matrixr1~X0~\\
X1)){\unicdcdcdhd}(m2\_finseq\_1~(k7\_matrixr1~X0~X1)~(k3\_finseq\_2~k1\_numbers)))\end{array}
\label{hyp:egehpflghdpfngbgehchjgihchbd}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdedpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehgdgdpfngbgehchjgihchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdbdjdcd}(k7\_matrixr1~X2~(k8\_matrixr1~X0~X1)=k8\_matrixr1~\\
X0~X1))))\end{array}$$
\end{theorem}
\end{document}
