\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{t33\_fsm\_3 (TMH5qsyQbGaQgupBZ3repJWKfMnN676tMsY)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ g1\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ u1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_fsm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh r1\_xboole\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in \\
X0){\unicdcdcdhd}(X2 \in X1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X2 .  (X2 \in X0){\unicdcdcdhd}(X2 \in X1)){\unicdcdcdhd}(r1\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ehddpfihcgpgpgmgfgpfad}
\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 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l2\_fsm\_3~\\
X2~X0~X1)){\unicdbdjdcd}(u1\_struct\_0~(k4\_fsm\_3~X0~X1~X2)=k1\_zfmisc\_1~(u1\_struct\_0~\\
X2))))\end{array}
\label{hyp:ehbdgdpfggdhngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_catalan2}~{X0}}={{k8\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdgbgehbgmgbgogcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k9\_flang\_1}~{X0}})}}~{({{k1\_zfmisc\_1}~{({{k3\_catalan2}~{X0}})}})}}}\label{hyp:egehpflgjdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(m1\_subset\_1~(k4\_subset\_1~\\
X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l2\_fsm\_3~\\
X2~X0~X1)))){\unicdbdjdcd}((v3\_fsm\_3~(k4\_fsm\_3~X0~X1~X2)~X0~(k9\_flang\_1~X0)){\unicdcdcdhd}\\
(l2\_fsm\_3~(k4\_fsm\_3~X0~X1~X2)~X0~(k9\_flang\_1~X0)))\end{array}
\label{hyp:egehpflgedpfggdhngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_catalan2~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k4\_flang\_1~X0~X1)~(k1\_zfmisc\_1~(k3\_catalan2~X0)))\end{array}
\label{hyp:egehpflgedpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k2\_flang\_1}~{X0}})}}~{({{k3\_catalan2}~{X0}})}}}\label{hyp:egehpflgcdpfggmgbgoghgpfbd}
\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 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l2\_fsm\_3~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_fsm\_3~X3~X0~(k9\_flang\_1~X0)){\unicdcdcdhd}(l2\_fsm\_3~\\
X3~X0~(k9\_flang\_1~X0))){\unicdbdjdcd}((X3=k4\_fsm\_3~X0~X1~X2){\unicdbdjded}((g1\_fsm\_3~X0~(\\
k9\_flang\_1~X0)~(u1\_struct\_0~X3)~(u1\_rewrite3~(k9\_flang\_1~X0)~X3)~\\
(u1\_fsm\_3~X0~(k9\_flang\_1~X0)~X3)=k2\_fsm\_3~X0~X1~(g1\_fsm\_3~X0~X1~(\\
u1\_struct\_0~X2)~(u1\_rewrite3~X1~X2)~(u1\_fsm\_3~X0~X1~X2))){\unicdcdcdhd}(u2\_fsm\_3~\\
X0~(k9\_flang\_1~X0)~X3=ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~\\
X4~(u1\_struct\_0~X3)))~({\uniddcgcg} X4 : \iota .  \preoh r1\_xboole\_0~X4~(u2\_fsm\_3~X0~\\
X1~X2))~({\uniddcgcg} X4 : \iota .  X4)))))))\end{array}
\label{hyp:eggdpfggdhngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddddpfggdhngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l2\_fsm\_3~X2~X1~(k4\_subset\_1~(k3\_catalan2~X1)~(k9\_flang\_1~\\
X1)~(k4\_flang\_1~X1~(k2\_flang\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X2))){\unicdbdjdcd}(((X0 \in u2\_fsm\_3~X1~(k4\_subset\_1~\\
(k3\_catalan2~X1)~(k9\_flang\_1~X1)~(k4\_flang\_1~X1~(k2\_flang\_1~X1)))~\\
X2){\unicdcdcdhd}(X0 \in X3)){\unicdbdjdcd}(X3 \in u2\_fsm\_3~X1~(k9\_flang\_1~X1)~(k4\_fsm\_3~X1~(k4\_subset\_1~\\
(k3\_catalan2~X1)~(k9\_flang\_1~X1)~(k4\_flang\_1~X1~(k2\_flang\_1~X1)))~\\
X2)))))\end{array}$$
\end{theorem}
\end{document}
