\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{t12\_fsm\_2 (TMV45JkBhw1Fvk3s2w31DGLg46V2QqCkW4F)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\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 $ v1\_fsm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u2\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_fsm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_fsm\_1~X1~X0)){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~X0){\unicdbdjdcd}(((k1\_funct\_1~X2~np\_\_1=k1\_funct\_1~X3~np\_\_1){\unicdcdcdhd}\\
(k3\_finseq\_1~X2=k3\_finseq\_1~X3)){\unicdbdjdcd}(k2\_fsm\_1~X0~X1~(u2\_fsm\_1~X0~\\
X1)~X2=k2\_fsm\_1~X0~X1~(u2\_fsm\_1~X0~X1)~X3)))){\unicdbdjdcd}(v1\_fsm\_2~X1~X0)))\end{array}
\label{hyp:ehhdpfggdhngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_fsm\_1~X1~X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_finseq\_1~X3~X0)))){\unicdbdjdcd}(m2\_finseq\_1~(k2\_fsm\_1~X0~X1~X2~X3)~\\
(u1\_struct\_0~X1))\end{array}
\label{hyp:egehpflgcdpfggdhngpfbd}
\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}\\
(l1\_fsm\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~(\\
u1\_struct\_0~X1)){\unicdbdjdcd}((X4=k2\_fsm\_1~X0~X1~X2~X3){\unicdbdjded}((k1\_funct\_1~X4~np\_\_1=\\
X2){\unicdcdcdhd}((k3\_finseq\_1~X4=k2\_nat\_1~(k3\_finseq\_1~X3)~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(v7\_ordinal1~X5){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X5){\unicdcdcdhd}((r1\_xxreal\_0~X5~(\\
k3\_finseq\_1~X3)){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}(\preoh (X6=k1\_funct\_1~X3~X5){\unicdcdcdhd}((X7=k1\_funct\_1~X4~\\
X5){\unicdcdcdhd}((X8=k1\_funct\_1~X4~(k1\_nat\_1~X5~np\_\_1)){\unicdcdcdhd}(k1\_fsm\_1~X0~X1~X6~\\
X7=X8)))))))))))))))))\end{array}
\label{hyp:egcdpfggdhngpfbd}
\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}\\
(l1\_fsm\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}(k1\_fsm\_1~X0~X1~X2~X3=k3\_funct\_2~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~X0)~(u1\_struct\_0~X1)~(u1\_fsm\_1~X0~\\
X1)~(k1\_domain\_1~(u1\_struct\_0~X1)~X0~X3~X2)))))\end{array}
\label{hyp:egbdpfggdhngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfggdhngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_fsm\_1~X1~X0)){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}(k3\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~X0)~(u1\_struct\_0~\\
X1)~(u1\_fsm\_1~X0~X1)~(k1\_domain\_1~(u1\_struct\_0~X1)~X0~X4~X2)=k3\_funct\_2~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~X0)~(u1\_struct\_0~X1)~(u1\_fsm\_1~X0~\\
X1)~(k1\_domain\_1~(u1\_struct\_0~X1)~X0~X4~X3))))){\unicdbdjdcd}(v1\_fsm\_2~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
