\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{t47\_matrix\_1 (TMSD7TGKHk92NeDb7PJUnKA4qxpo6eAqfgZ)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ 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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k16\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}(k16\_matrix\_1~X1=ReplSep2~\\
(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k5\_numbers))~({\uniddcgcg} X2 : \iota .  \\
toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k5\_numbers))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  k4\_tarski~X2~X3 \in k2\_matrix\_1~X1)~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  \\
k3\_matrix\_1~X0~X1~X2~X3)))\end{array}
\label{hyp:ehedfdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_matrix\_1~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~\\
X0))){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~X1~(k3\_finseq\_1~\\
X3)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k1\_matrix\_1~X3))))){\unicdbdjdcd}\\
(k4\_tarski~X1~X2 \in k2\_matrix\_1~X3))))\end{array}
\label{hyp:ehddgdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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:ehedhdpfngbgehchjgihpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_matrix\_1~\\
X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~X0))){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~\\
X1){\unicdcdcdhd}((r1\_xxreal\_0~X1~(k3\_finseq\_1~X3)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}\\
(r1\_xxreal\_0~X2~(k1\_matrix\_1~X3))))){\unicdbdjdcd}(k3\_matrix\_1~X0~X3~X1~X2 \in \\
k16\_matrix\_1~X3)))))\end{array}$$
\end{theorem}
\end{document}
