\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{t24\_rewrite3 (TMV6BDTwgjc2VKbxz42NM576JAUfb1YgHP4)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r2\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ k1\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(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}((k1\_flang\_1~X0~X1~X2=k1\_flang\_1~X0~X3~X4){\unicdbdjdcd}(\\
((k1\_afinsq\_1~X1{\unicdcdgdad}k1\_afinsq\_1~X3){\unicdcdcdhd}(k1\_afinsq\_1~X2{\unicdcdgdad}k1\_afinsq\_1~\\
X4)){\unicdcdcdid}((X1=X3){\unicdcdcdhd}(X2=X4))))))))\end{array}
\label{hyp:ehbdbdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k8\_afinsq\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_rewrite3~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  (r2\_rewrite3~X0~X1~X2~X3~X4~X5~X6){\unicdbdjded}\\
({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(k8\_afinsq\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~\\
X8~(k8\_afinsq\_1~X0)){\unicdcdcdhd}((X7=X6){\unicdcdcdhd}((r1\_rewrite3~X1~X2~X3~X8~X5){\unicdcdcdhd}(X4=\\
k1\_flang\_1~X0~X8~X7))))))))\end{array}
\label{hyp:egddpfchfghhchjgehfgdd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(\\
k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X6 .  (l1\_rewrite3~X6~X5){\unicdbdjdcd}((r1\_rewrite3~\\
X5~X6~X0~X3~X1){\unicdbdjded}(r2\_rewrite3~X2~X5~X6~X0~(k1\_flang\_1~X2~X3~X4)~X1~X4))))))\end{array}$$
\end{theorem}
\end{document}
