\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}
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\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{t5\_dynkin (TMUWoZRMMTBEjugsnUaYA2SQH2C9J5QGrub)}
\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_dynkin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_dynkin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
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 .  ((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 .  ((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}((X2=k4\_dynkin~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}\\
(k8\_nat\_1~(k9\_setfam\_1~X0)~X2~X3=k3\_dynkin~X0~X1~X3)))))\end{array}
\label{hyp:egedpfegjhoglgjgog}
\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 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k3\_dynkin~X0~X1~X2=k7\_subset\_1~X0~\\
(k8\_nat\_1~(k9\_setfam\_1~X0)~X1~X2)~(k3\_tarski~(k10\_xtuple\_0~(k5\_relat\_1~\\
X1~X2))))))\end{array}
\label{hyp:egddpfegjhoglgjgog}
\end{equation}
\begin{theorem}\label{thm:ehfdpfegjhoglgjgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k8\_nat\_1~(k9\_setfam\_1~X0)~(k4\_dynkin~\\
X0~X1)~X2=k7\_subset\_1~X0~(k8\_nat\_1~(k9\_setfam\_1~X0)~X1~X2)~(k3\_tarski~\\
(k10\_xtuple\_0~(k5\_relat\_1~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
