\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{t37\_fsm\_3 (TMFa99mHhEDwsZGxV2D2oFwZrpLHawYGFEs)}
\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 $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_catalan2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k4\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k8\_afinsq\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(l2\_fsm\_3~\\
X3~X1~(k4\_subset\_1~(k3\_catalan2~X1)~(k9\_flang\_1~X1)~(k4\_flang\_1~\\
X1~(k2\_flang\_1~X1))))){\unicdbdjdcd}(k3\_rewrite3~X1~(k9\_flang\_1~X1)~(k4\_fsm\_3~\\
X1~(k4\_subset\_1~(k3\_catalan2~X1)~(k9\_flang\_1~X1)~(k4\_flang\_1~X1~\\
(k2\_flang\_1~X1)))~X3)~X2~(k6\_domain\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X3))~(k3\_rewrite3~X1~(k4\_subset\_1~(k3\_catalan2~X1)~(k9\_flang\_1~\\
X1)~(k4\_flang\_1~X1~(k2\_flang\_1~X1)))~X3~(k2\_flang\_1~X1)~X0))=k6\_domain\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X3))~(k3\_rewrite3~X1~(k4\_subset\_1~(\\
k3\_catalan2~X1)~(k9\_flang\_1~X1)~(k4\_flang\_1~X1~(k2\_flang\_1~X1)))~\\
X3~X2~X0))))\end{array}
\label{hyp:ehddgdpfggdhngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l2\_fsm\_3~X1~X0~(k4\_subset\_1~(k3\_catalan2~X0)~(k9\_flang\_1~X0)~(\\
k4\_flang\_1~X0~(k2\_flang\_1~X0))))){\unicdbdjdcd}(u1\_fsm\_3~X0~(k9\_flang\_1~X0)~\\
(k4\_fsm\_3~X0~(k4\_subset\_1~(k3\_catalan2~X0)~(k9\_flang\_1~X0)~(k4\_flang\_1~\\
X0~(k2\_flang\_1~X0)))~X1)=k6\_domain\_1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))~(k3\_rewrite3~X0~(k4\_subset\_1~(k3\_catalan2~X0)~(k9\_flang\_1~\\
X0)~(k4\_flang\_1~X0~(k2\_flang\_1~X0)))~X1~(k2\_flang\_1~X0)~(u1\_fsm\_3~\\
X0~(k4\_subset\_1~(k3\_catalan2~X0)~(k9\_flang\_1~X0)~(k4\_flang\_1~X0~\\
(k2\_flang\_1~X0)))~X1))))\end{array}
\label{hyp:ehddfdpfggdhngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfggdhngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k8\_afinsq\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l2\_fsm\_3~X2~X0~(k4\_subset\_1~\\
(k3\_catalan2~X0)~(k9\_flang\_1~X0)~(k4\_flang\_1~X0~(k2\_flang\_1~X0))))){\unicdbdjdcd}\\
(k3\_rewrite3~X0~(k9\_flang\_1~X0)~(k4\_fsm\_3~X0~(k4\_subset\_1~(k3\_catalan2~\\
X0)~(k9\_flang\_1~X0)~(k4\_flang\_1~X0~(k2\_flang\_1~X0)))~X2)~X1~(u1\_fsm\_3~\\
X0~(k9\_flang\_1~X0)~(k4\_fsm\_3~X0~(k4\_subset\_1~(k3\_catalan2~X0)~(\\
k9\_flang\_1~X0)~(k4\_flang\_1~X0~(k2\_flang\_1~X0)))~X2))=k6\_domain\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X2))~(k3\_rewrite3~X0~(k4\_subset\_1~(\\
k3\_catalan2~X0)~(k9\_flang\_1~X0)~(k4\_flang\_1~X0~(k2\_flang\_1~X0)))~\\
X2~X1~(u1\_fsm\_3~X0~(k4\_subset\_1~(k3\_catalan2~X0)~(k9\_flang\_1~X0)~\\
(k4\_flang\_1~X0~(k2\_flang\_1~X0)))~X2)))))\end{array}$$
\end{theorem}
\end{document}
