\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{t45\_rewrite3 (TMHmz3uTfUBzo1y3UNjDrMLda26EHtWpSaj)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(k8\_afinsq\_1~X3))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~X5){\unicdcdcdhd}(l1\_rewrite3~X5~X4)){\unicdbdjdcd}(((v2\_rewrite3~\\
X5~X3~X4){\unicdcdcdhd}((k4\_tarski~X0~X1 \in k1\_rewrite3~X3~X4~X5){\unicdcdcdhd}(k4\_tarski~X0~\\
X2 \in k1\_rewrite3~X3~X4~X5))){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehededpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1=\\
k4\_tarski~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3))\end{array}
\label{hyp:ehbdpfihehfhahmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(\preoh v1\_xboole\_0~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~(\\
k8\_afinsq\_1~X5))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((\preoh v2\_struct\_0~X7){\unicdcdcdhd}(l1\_rewrite3~\\
X7~X6)){\unicdbdjdcd}(((v2\_rewrite3~X7~X5~X6){\unicdcdcdhd}((k4\_tarski~X0~(k4\_tarski~X1~X2) \in \\
k1\_rewrite3~X5~X6~X7){\unicdcdcdhd}(k4\_tarski~X0~(k4\_tarski~X3~X4) \in k1\_rewrite3~\\
X5~X6~X7))){\unicdbdjdcd}((X1=X3){\unicdcdcdhd}(X2=X4)))))\end{array}$$
\end{theorem}
\end{document}
