\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}
\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{t29\_rewrite2 (TMH5RJ7TAnBG4dY9QgMAMaH7XaJWeYjjYPg)}
\maketitle
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_rewrite2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_partit\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_rewrite2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k8\_afinsq\_1~X0)){\unicdbdjdcd}(\preoh r2\_rewrite2~X0~(k1\_partit\_2~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0))~X1~X2))\end{array}
\label{hyp:ehcdadpfchfghhchjgehfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  m1\_subset\_1~(k1\_partit\_2~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:egehpflgbdpfahbgchehjgehpfcd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k1\_partit\_2}~{X0}}~{X1}}={k1\_xboole\_0}}}}\label{hyp:egbdpfahbgchehjgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfchfghhchjgehfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  r2\_relset\_1~(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)~(k7\_rewrite2~\\
X0~(k1\_partit\_2~(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0)))~(k1\_partit\_2~\\
(k8\_afinsq\_1~X0)~(k8\_afinsq\_1~X0))\end{array}$$
\end{theorem}
\end{document}
