\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{t29\_fsm\_2 (TMGb4nzU6fh31QkzWmLcVmUGiGESvScpSiF)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v5\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_square\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_fsm\_2~X0~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)~(k1\_ordinal1~k1\_numbers))){\unicdbdjdcd}(((v1\_fsm\_2~X0~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)){\unicdcdcdhd}((u1\_struct\_0~X0=k1\_ordinal1~k1\_numbers){\unicdcdcdhd}\\
((u1\_fsm\_2~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0=k1\_numbers){\unicdcdcdhd}\\
((u2\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0=k1\_numbers){\unicdcdcdhd}\\
((u4\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~(k1\_ordinal1~\\
k1\_numbers)~X0=k6\_partfun1~(u1\_struct\_0~X0)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
((\preoh r1\_xxreal\_0~X2~X1){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))~(u1\_struct\_0~X0)~(u1\_fsm\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0)~(k1\_domain\_1~(u1\_struct\_0~\\
X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~(u2\_fsm\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)~X0)~(k1\_domain\_1~k1\_numbers~k1\_numbers~\\
X1~X2))=X1)))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X2~X1){\unicdbdjdcd}(k3\_funct\_2~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))~\\
(u1\_struct\_0~X0)~(u1\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~\\
X0)~(k1\_domain\_1~(u1\_struct\_0~X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~\\
(u2\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0)~(k1\_domain\_1~\\
k1\_numbers~k1\_numbers~X1~X2))=X2)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(r3\_fsm\_2~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~(k1\_ordinal1~k1\_numbers)~\\
X0~(k1\_domain\_1~k1\_numbers~k1\_numbers~X1~X2)~(k1\_square\_1~X1~X2)))))\end{array}
\label{hyp:ehcdedpfggdhngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X1){\unicdbdjdcd}(v1\_xboole\_0~(k2\_zfmisc\_1~\\
X0~X1))\end{array}
\label{hyp:ggdgddpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_ordinal1}~{X0}})}}}}}\label{hyp:ggdgbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:ggdgbdadpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_fsm\_1~X1~X0){\unicdbdjdcd}(m1\_subset\_1~(u2\_fsm\_1~\\
X0~X1)~(u1\_struct\_0~X1))\end{array}
\label{hyp:egehpffhcdpfggdhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_fsm\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_fsm\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(u1\_fsm\_1~X0~X1)~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~(u1\_fsm\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~X0)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpffhbdpfggdhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (l2\_fsm\_2~\\
X2~X0~X1){\unicdbdjdcd}((l1\_fsm\_2~X2~X0){\unicdcdcdhd}(l3\_fsm\_1~X2~X0~X1)))\end{array}
\label{hyp:egehpfmgcdpfggdhngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{l1\_fsm\_2}~{X1}}~{X0}})}{\unicdbdjdcd}{({{{l1\_fsm\_1}~{X1}}~{X0}})}}}}\label{hyp:egehpfmgbdpfggdhngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(m1\_subset\_1~(\\
k3\_funct\_2~X0~X1~X2~X3)~X1)\end{array}
\label{hyp:egehpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_numbers)){\unicdbdjdcd}(m1\_subset\_1~(k1\_square\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_domain\_1~X0~X1~X2~X3)~(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:egehpflgbdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_fsm\_2~X2~X0){\unicdcdcdhd}((v5\_fsm\_2~\\
X2~X0){\unicdcdcdhd}(l2\_fsm\_2~X2~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X1){\unicdbdjdcd}((X4=k2\_fsm\_2~X0~X1~X2~X3){\unicdbdjded}(r3\_fsm\_2~\\
X0~X1~X2~X3~X4))))))\end{array}
\label{hyp:egjdpfggdhngpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfggdhngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_fsm\_2~X0~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)){\unicdcdcdhd}((v5\_fsm\_2~X0~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)){\unicdcdcdhd}\\
(l2\_fsm\_2~X0~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~(k1\_ordinal1~\\
k1\_numbers))))){\unicdbdjdcd}(((u1\_struct\_0~X0=k1\_ordinal1~k1\_numbers){\unicdcdcdhd}\\
((u1\_fsm\_2~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0=k1\_numbers){\unicdcdcdhd}\\
((u2\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0=k1\_numbers){\unicdcdcdhd}\\
((u4\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~(k1\_ordinal1~\\
k1\_numbers)~X0=k6\_partfun1~(u1\_struct\_0~X0)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
((\preoh r1\_xxreal\_0~X2~X1){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))~(u1\_struct\_0~X0)~(u1\_fsm\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0)~(k1\_domain\_1~(u1\_struct\_0~\\
X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~(u2\_fsm\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)~X0)~(k1\_domain\_1~k1\_numbers~k1\_numbers~\\
X1~X2))=X1)))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X2~X1){\unicdbdjdcd}(k3\_funct\_2~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))~\\
(u1\_struct\_0~X0)~(u1\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~\\
X0)~(k1\_domain\_1~(u1\_struct\_0~X0)~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~\\
(u2\_fsm\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~X0)~(k1\_domain\_1~\\
k1\_numbers~k1\_numbers~X1~X2))=X2))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(k2\_fsm\_2~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)~(k1\_ordinal1~k1\_numbers)~\\
X0~(k1\_domain\_1~k1\_numbers~k1\_numbers~X1~X2)=k1\_square\_1~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
