\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{l9\_petri\_2 (TMZ4jcfVwSxRQzX5mcBATfy1abwSRQrc8nS)}
\maketitle
Let $ v1\_zfmisc\_1 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_zfmisc\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X0))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X3~X0))))){\unicdbdjdcd}(\preoh (X2{\unicdcdgdad}X3){\unicdcdcdhd}((r1\_tarski~X3~X2){\unicdcdcdhd}({\unicdcdadad} X6 .  ((v1\_funct\_1~\\
X6){\unicdcdcdhd}((v1\_funct\_2~X6~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdbdjdcd}(\preoh (k2\_partfun1~X1~X0~X6~X3=X5){\unicdcdcdhd}(k2\_partfun1~X1~X0~X6~\\
X2{\unicdcdgdad}X4)))))))))\end{array}
\label{hyp:mgidpfahfgehchjgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_zfmisc\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X0))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X3~X0))))){\unicdbdjdcd}(\preoh (\preoh r1\_tarski~X3~X2){\unicdcdcdhd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}\\
((v1\_funct\_2~X6~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdbdjdcd}(\preoh (k2\_partfun1~X1~X0~X6~X2=X4){\unicdcdcdhd}(k2\_partfun1~X1~X0~X6~\\
X3{\unicdcdgdad}X5))))))))\end{array}
\label{hyp:mghdpfahfgehchjgpfcd}
\end{equation}
\begin{theorem}\label{thm:mgjdpfahfgehchjgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_zfmisc\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X0))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X3~X0))))){\unicdbdjdcd}(\preoh (X2{\unicdcdgdad}X3){\unicdcdcdhd}(ReplSep~(toset~({\uniddcgcg} X6 : \iota .  (v1\_funct\_1~\\
X6){\unicdcdcdhd}((v1\_funct\_2~X6~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))))~({\uniddcgcg} X6 : \iota .  k2\_partfun1~X1~X0~X6~X2=X4)~({\uniddcgcg} X6 : \iota .  \\
X6)=ReplSep~(toset~({\uniddcgcg} X6 : \iota .  (v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))))~\\
({\uniddcgcg} X6 : \iota .  k2\_partfun1~X1~X0~X6~X3=X5)~({\uniddcgcg} X6 : \iota .  X6)))))))\end{array}$$
\end{theorem}
\end{document}
