\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{l22\_fomodel3 (TMZvQMqwLFcYN2giN6tgwiQmPCn8zxrsxYE)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_relat\_2~X1){\unicdcdcdhd}(\\
(v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k8\_eqrel\_1~X0~X1)))\end{array}
\label{hyp:ehgdedpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v3\_relat\_2~\\
X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}((v1\_partfun1~X2~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k1\_zfmisc\_1~\\
X1)~(k8\_eqrel\_1~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~(k1\_zfmisc\_1~\\
X1)~(k8\_eqrel\_1~X1~X2)){\unicdbdjdcd}(((X0 \in X3){\unicdcdcdhd}(X0 \in X4)){\unicdbdjdcd}(X3=X4)))))\end{array}
\label{hyp:ehddpfahchbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v3\_relat\_2~X3){\unicdcdcdhd}\\
((v1\_partfun1~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))))){\unicdbdjdcd}((X1 \in k6\_eqrel\_1~X0~X0~X3~X2){\unicdbdjded}(k4\_tarski~X1~X2 \in X3))\end{array}
\label{hyp:ehbdjdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v3\_relat\_2~\\
X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k9\_eqrel\_1~X0~\\
X1~X2=k9\_relat\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k6\_eqrel\_1~X0~X1~X2~X3=k9\_relat\_1~\\
X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (\\
m2\_subset\_1~X4~(k1\_zfmisc\_1~X0)~(k8\_eqrel\_1~X0~X1)){\unicdbdjdcd}(((X2 \in X4){\unicdcdcdhd}\\
(X3 \in X4)){\unicdbdjdcd}(k4\_tarski~X2~X3 \in X1))))\end{array}
\label{hyp:mgcdbdpfggpgngpgegfgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))\end{array}
\label{hyp:egehpfngbdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v3\_relat\_2~\\
X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(m2\_subset\_1~\\
(k9\_eqrel\_1~X0~X1~X2)~(k1\_zfmisc\_1~X0)~(k8\_eqrel\_1~X0~X1))\end{array}
\label{hyp:egehpflgjdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}\\
(m1\_eqrel\_1~(k8\_eqrel\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgidpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mgcdcdpfggpgngpgegfgmgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v3\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)~(k8\_eqrel\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k1\_zfmisc\_1~\\
X0)~(k8\_eqrel\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  ((X4 \in X2){\unicdcdcdhd}((X5 \in \\
X3){\unicdcdcdhd}(k4\_tarski~X4~X5 \in X1))){\unicdbdjdcd}(X2=X3)))))\end{array}$$
\end{theorem}
\end{document}
