\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{t17\_dynkin (TMHN6cwHGCScr9YWtt62cexx7d7fm8soRr9)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_dynkin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_finsub\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_dynkin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_prob\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}(\\
k3\_tarski~(k10\_xtuple\_0~(k4\_dynkin~X0~X1))=k3\_tarski~(k10\_xtuple\_0~\\
X1)))\end{array}
\label{hyp:ehhdpfegjhoglgjgog}
\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}(\\
v1\_prob\_2~(k4\_dynkin~X0~X1)))\end{array}
\label{hyp:ehgdpfegjhoglgjgog}
\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){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}(((m1\_dynkin~\\
X1~X0){\unicdcdcdhd}(v2\_finsub\_1~X1)){\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}((r1\_tarski~(\\
k10\_xtuple\_0~X2)~X1){\unicdbdjdcd}(r1\_tarski~(k10\_xtuple\_0~(k4\_dynkin~X0~X2))~\\
X1)))))\end{array}
\label{hyp:ehbdgdpfegjhoglgjgog}
\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 .  ((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}(k1\_prob\_1~X0~X1=k3\_card\_3~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_dynkin~X1~X0){\unicdbdjdcd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))))\end{array}
\label{hyp:egehpfngbdpfegjhoglgjgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\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))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k4\_dynkin~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k4\_dynkin~X0~X1)~\\
k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k4\_dynkin~X0~X1)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0))))))\end{array}
\label{hyp:egehpflgedpfegjhoglgjgog}
\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~\\
(k1\_zfmisc\_1~X0))){\unicdbdjdcd}((m1\_dynkin~X1~X0){\unicdbdjded}(({\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}\\
(((r1\_tarski~(k10\_xtuple\_0~X2)~X1){\unicdcdcdhd}(v1\_prob\_2~X2)){\unicdbdjdcd}(k1\_prob\_1~\\
X0~X2 \in X1))){\unicdcdcdhd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(\\
(X2 \in X1){\unicdbdjdcd}(k3\_subset\_1~X0~X2 \in X1))){\unicdcdcdhd}(k1\_xboole\_0 \in X1)))))\end{array}
\label{hyp:egfdpfegjhoglgjgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(k3\_card\_3~X0=\\
k3\_tarski~(k10\_xtuple\_0~X0))\end{array}
\label{hyp:egedpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_dynkin~X1~X0){\unicdbdjdcd}(\\
\preoh v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfegjhoglgjgog}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfegjhoglgjgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}(((m1\_dynkin~\\
X1~X0){\unicdcdcdhd}(v2\_finsub\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}((r1\_tarski~(\\
k10\_xtuple\_0~X2)~X1){\unicdbdjdcd}(k3\_tarski~(k10\_xtuple\_0~X2) \in X1)))))\end{array}$$
\end{theorem}
\end{document}
