\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{t97\_matrixr2 (TMRT5su9YrgXxTNnxKoHn3awW2csJBZCGGA)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_matrixr2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_matrixr2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_matrixr2 : {{\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\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
(m2\_finseq\_1~X2~k1\_numbers){\unicdbdjdcd}(\preoh (k3\_finseq\_1~X2=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~k1\_numbers){\unicdbdjdcd}(\preoh (k3\_finseq\_1~X3=X0){\unicdcdcdhd}(k11\_matrixr1~\\
X1~X3=X2))))){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~k1\_numbers~X0~X0){\unicdbdjdcd}(\\
k1\_matrixr2~X0~X1~X2{\unicdcdgdad}k4\_matrixr2~X0)))))\end{array}
\label{hyp:ehjdgdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}(\preoh ({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k1\_numbers){\unicdbdjdcd}\\
(\preoh (k3\_finseq\_1~X2=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~k1\_numbers){\unicdbdjdcd}\\
(\preoh (k3\_finseq\_1~X3=X0){\unicdcdcdhd}(k12\_matrixr1~X1~X3=X2))))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_matrix\_1~X2~k1\_numbers~X0~X0){\unicdbdjdcd}(k1\_matrixr2~X0~X2~X1{\unicdcdgdad}k4\_matrixr2~\\
X0))))\end{array}
\label{hyp:ehjdddpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~k1\_numbers~X0~\\
X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~k1\_numbers~X0~X0){\unicdbdjdcd}(((k1\_matrixr2~\\
X0~X2~X1=k4\_matrixr2~X0){\unicdcdcdhd}(k1\_matrixr2~X0~X1~X3=k4\_matrixr2~X0)){\unicdbdjdcd}\\
((X2=X3){\unicdcdcdhd}(v1\_matrixr2~X1~X0))))))\end{array}
\label{hyp:ehidadpfngbgehchjgihchcd}
\end{equation}
\begin{theorem}\label{thm:ehjdhdpfngbgehchjgihchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_matrix\_1~\\
X1~k1\_numbers~X0~X0){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k1\_numbers){\unicdbdjdcd}\\
(\preoh (k3\_finseq\_1~X2=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~k1\_numbers){\unicdbdjdcd}(\preoh (k3\_finseq\_1~X3=X0){\unicdcdcdhd}\\
((k3\_finseq\_1~X4=X0){\unicdcdcdhd}((k11\_matrixr1~X1~X3=X2){\unicdcdcdhd}(k12\_matrixr1~\\
X1~X4=X2)))))))){\unicdbdjdcd}((r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdid}(v1\_matrixr2~\\
X1~X0))))\end{array}$$
\end{theorem}
\end{document}
