\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{t50\_afproj (TMUsqUkSA3m7XZiS9JyNJws5TLMs6zAKmrC)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((X1 \in X6){\unicdcdcdhd}((X1 \in X7){\unicdcdcdhd}((X2 \in X6){\unicdcdcdhd}\\
((X3 \in X6){\unicdcdcdhd}((X4 \in X7){\unicdcdcdhd}((X5 \in X7){\unicdcdcdhd}((v1\_aff\_1~X6~X0){\unicdcdcdhd}((v1\_aff\_1~X7~\\
X0){\unicdcdcdhd}(X2=X3))))))))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}((X1=X4){\unicdcdcdid}((X6=X7){\unicdcdcdid}(((\preoh r2\_analoaf~\\
X0~X2~X4~X3~X5){\unicdcdcdhd}(\preoh r2\_analoaf~X0~X4~X2~X5~X3)){\unicdcdcdid}(X4=X5)))))))))))))\end{array}
\label{hyp:ehjdpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((X1 \in X6){\unicdcdcdhd}((X1 \in X7){\unicdcdcdhd}((X2 \in X6){\unicdcdcdhd}\\
((X3 \in X7){\unicdcdcdhd}((X4 \in X7){\unicdcdcdhd}((v1\_aff\_1~X6~X0){\unicdcdcdhd}((v1\_aff\_1~X7~X0){\unicdcdcdhd}(X1=X5)))))))){\unicdbdjdcd}\\
((X1=X2){\unicdcdcdid}((X1=X3){\unicdcdcdid}((X6=X7){\unicdcdcdid}(((\preoh r2\_analoaf~X0~X2~X3~X5~X4){\unicdcdcdhd}(\preoh \\
r2\_analoaf~X0~X3~X2~X4~X5)){\unicdcdcdid}(X1=X4)))))))))))))\end{array}
\label{hyp:ehidpfbgggggpfed}
\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 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X3~X3){\unicdcdcdhd}(r2\_analoaf~X0~X3~X3~X1~X2)))))\end{array}
\label{hyp:ehddpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X2~X1){\unicdcdcdhd}(r2\_analoaf~X0~\\
X1~X2~X1~X2))))\end{array}
\label{hyp:ehcdpfbgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(((X4 \in X1){\unicdcdcdhd}((X4 \in X2){\unicdcdcdhd}((X4 \in X3){\unicdcdcdhd}((X5 \in X1){\unicdcdcdhd}((X6 \in X2){\unicdcdcdhd}((X9 \in \\
X2){\unicdcdcdhd}((X7 \in X3){\unicdcdcdhd}((X10 \in X3){\unicdcdcdhd}((v1\_aff\_1~X1~X0){\unicdcdcdhd}((v1\_aff\_1~X2~X0){\unicdcdcdhd}\\
((v1\_aff\_1~X3~X0){\unicdcdcdhd}((r2\_analoaf~X0~X5~X6~X8~X9){\unicdcdcdhd}(r2\_analoaf~X0~X5~\\
X7~X8~X10))))))))))))){\unicdbdjdcd}((X4=X5){\unicdcdcdid}((X4=X6){\unicdcdcdid}((X4=X7){\unicdcdcdid}((X1=X2){\unicdcdcdid}\\
((X1=X3){\unicdcdcdid}(((X4{\unicdcdgdad}X8){\unicdcdcdhd}(X5{\unicdcdgdad}X8)){\unicdcdcdid}(r2\_analoaf~X0~X6~X7~X9~X10))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
