\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{l23\_petri\_2 (TMaQ96oSDd9QgepQg33ooKRtbKtufpawbVW)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k3\_xboole\_0}~{X0}}~{k1\_xboole\_0}}={k1\_xboole\_0}}}\label{hyp:ehcdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
(k1\_funct\_4~X2~X1)~X0=k1\_funct\_1~X1~X0)))\end{array}
\label{hyp:ehbdddpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((\preoh X0 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
(k1\_funct\_4~X2~X1)~X0=k1\_funct\_1~X2~X0)))\end{array}
\label{hyp:ehbdbdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{v1\_xboole\_0}~{X0}}}\label{hyp:chdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_4~X0~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_4~X0~X1)))\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mgcdddpfahfgehchjgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}(((k3\_xboole\_0~\\
(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X1)=k1\_xboole\_0){\unicdcdcdhd}((k3\_xboole\_0~\\
(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X2)=k1\_xboole\_0){\unicdcdcdhd}((k3\_xboole\_0~\\
(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X3)=k1\_xboole\_0){\unicdcdcdhd}((k3\_xboole\_0~\\
(k9\_xtuple\_0~X1)~(k9\_xtuple\_0~X2)=k1\_xboole\_0){\unicdcdcdhd}((k3\_xboole\_0~\\
(k9\_xtuple\_0~X1)~(k9\_xtuple\_0~X3)=k1\_xboole\_0){\unicdcdcdhd}((k3\_xboole\_0~\\
(k9\_xtuple\_0~X2)~(k9\_xtuple\_0~X3)=k1\_xboole\_0){\unicdcdcdhd}(X4=k1\_funct\_4~\\
(k1\_funct\_4~(k1\_funct\_4~X0~X1)~X2)~X3))))))){\unicdbdjdcd}(({\unicdcdadad} X5 .  (X5 \in \\
k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k1\_funct\_1~X0~X5)){\unicdcdcdhd}(({\unicdcdadad} X5 .  \\
(X5 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k1\_funct\_1~X1~X5)){\unicdcdcdhd}(({\unicdcdadad} X5 .  \\
(X5 \in k9\_xtuple\_0~X2){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k1\_funct\_1~X2~X5)){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(X5 \in k9\_xtuple\_0~X3){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k1\_funct\_1~X3~X5))))))))))\end{array}$$
\end{theorem}
\end{document}
