\documentclass{article}
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\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t30\_rewrite2 (TMGYG5bPMgmMkvMvZxJr1UDD7KWAmAovcfZ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_rewrite2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_rewrite2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_rewrite2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k8\_afinsq\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k8\_afinsq\_1~X0)){\unicdbdjdcd}((r2\_rewrite2~X0~X1~X2~X3){\unicdbdjdcd}(\\
r2\_rewrite2~X0~X1~(k1\_flang\_1~X0~(k1\_flang\_1~X0~X4~X2)~X5)~(k1\_flang\_1~\\
X0~(k1\_flang\_1~X0~X4~X3)~X5)))))))\end{array}
\label{hyp:ehbdddpfchfghhchjgehfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k7\_rewrite2~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~\\
X0))))\end{array}
\label{hyp:egehpflghdpfchfghhchjgehfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))){\unicdbdjdcd}\\
((X2=k7\_rewrite2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k8\_afinsq\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k8\_afinsq\_1~X0)){\unicdbdjdcd}((k1\_domain\_1~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)~X3~X4 \in X2){\unicdbdjded}(r2\_rewrite2~X0~X1~\\
X3~X4))))))\end{array}
\label{hyp:eggdpfchfghhchjgehfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k8\_afinsq\_1~\\
X0)){\unicdbdjdcd}((r2\_rewrite2~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(k8\_afinsq\_1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k8\_afinsq\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~(k8\_afinsq\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~\\
(k8\_afinsq\_1~X0)){\unicdcdcdhd}((X2=k1\_flang\_1~X0~(k1\_flang\_1~X0~X4~X6)~X5){\unicdcdcdhd}\\
((X3=k1\_flang\_1~X0~(k1\_flang\_1~X0~X4~X7)~X5){\unicdcdcdhd}(r1\_rewrite2~X0~X1~\\
X6~X7))))))))))\end{array}
\label{hyp:egfdpfchfghhchjgehfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k8\_afinsq\_1~\\
X0)){\unicdbdjdcd}((r1\_rewrite2~X0~X1~X2~X3){\unicdbdjded}(k1\_domain\_1~(k8\_afinsq\_1~X0)~\\
(k8\_afinsq\_1~X0)~X2~X3 \in X1))))\end{array}
\label{hyp:egedpfchfghhchjgehfgcd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfchfghhchjgehfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k8\_afinsq\_1~\\
X0)){\unicdbdjdcd}((r2\_rewrite2~X0~(k7\_rewrite2~X0~X1)~X2~X3){\unicdbdjdcd}(r2\_rewrite2~\\
X0~X1~X2~X3))))\end{array}$$
\end{theorem}
\end{document}
