\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{t10\_dynkin (TMKNH3wmRg3Nd4gGn9ppcVfEGB1NtENb4PE)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k5\_numbers : {\iota}$ be given.
Let $ k9\_setfam\_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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_dynkin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_setlim\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~\\
X0)))))){\unicdbdjdcd}(k1\_prob\_1~X0~(k5\_setlim\_2~X0~X2~X1)=k9\_subset\_1~X0~X1~\\
(k1\_prob\_1~X0~X2)))\end{array}
\label{hyp:ehddidpfdhfgehmgjgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}((v1\_funct\_1~(k2\_dynkin~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_dynkin~X0~X1~X2)~k5\_numbers~(k9\_setfam\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k2\_dynkin~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(k9\_setfam\_1~X0))))))\end{array}
\label{hyp:egehpflgcdpfegjhoglgjgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~\\
(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}((X3=k5\_setlim\_2~\\
X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(k8\_nat\_1~(\\
k9\_setfam\_1~X0)~X3~X4=k9\_subset\_1~X0~X2~(k8\_nat\_1~(k9\_setfam\_1~\\
X0)~X1~X4))))))\end{array}
\label{hyp:egfdpfdhfgehmgjgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}\\
((X3=k2\_dynkin~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}\\
(k8\_nat\_1~(k9\_setfam\_1~X0)~X3~X4=k9\_subset\_1~X0~X2~(k8\_nat\_1~(k9\_setfam\_1~\\
X0)~X1~X4)))))))\end{array}
\label{hyp:egbdpfegjhoglgjgog}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfegjhoglgjgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k9\_subset\_1~X0~\\
X2~(k1\_prob\_1~X0~X1)=k1\_prob\_1~X0~(k2\_dynkin~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
