\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{l31\_homothet (TMNPTd69vnuGKDhJSUKvCCzhZYbXNu1jA3M)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v7\_aff\_2 : {{\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 .  {\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~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(\preoh (r2\_aff\_1~X0~X1~X2~X3){\unicdcdcdhd}((\preoh X1 \in X3){\unicdcdcdhd}(X2 \in X3))))))\end{array}
\label{hyp:ehddfdpfbgggggpfbd}
\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~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((r2\_aff\_1~X0~X1~X2~X3){\unicdbdjdcd}(r2\_aff\_1~X0~X2~X1~X3)))))\end{array}
\label{hyp:ehddedpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_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~(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~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((r2\_aff\_1~\\
X0~X1~X2~X10){\unicdcdcdhd}((v7\_aff\_2~X0){\unicdcdcdhd}((X4 \in X10){\unicdcdcdhd}((X5 \in X10){\unicdcdcdhd}((r2\_analoaf~\\
X0~X4~X1~X5~X3){\unicdcdcdhd}((r2\_analoaf~X0~X4~X2~X5~X6){\unicdcdcdhd}((r2\_aff\_1~X0~X3~X6~X10){\unicdcdcdhd}\\
((X7 \in X10){\unicdcdcdhd}((X8 \in X10){\unicdcdcdhd}((r2\_analoaf~X0~X7~X1~X8~X3){\unicdcdcdhd}((r2\_aff\_1~X0~\\
X3~X9~X10){\unicdcdcdhd}(r2\_analoaf~X0~X7~X2~X8~X9)))))))))))){\unicdbdjdcd}((X1 \in X10){\unicdcdcdid}((\\
X3 \in X10){\unicdcdcdid}(X9=X6))))))))))))))\end{array}
\label{hyp:mgddadpfigpgngpgehigfgeh}
\end{equation}
\begin{theorem}\label{thm:mgddbdpfigpgngpgehigfgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_diraf~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((r2\_aff\_1~X0~X1~X2~X6){\unicdcdcdhd}(v7\_aff\_2~X0)){\unicdbdjdcd}((X1 \in X6){\unicdcdcdid}(((\preoh (X3 \in X6){\unicdcdcdhd}\\
(X3=X4)){\unicdcdcdhd}(\preoh (\preoh X3 \in X6){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdcdcdhd}((X7 \in X6){\unicdcdcdhd}\\
((X8 \in X6){\unicdcdcdhd}((r2\_analoaf~X0~X7~X1~X8~X3){\unicdcdcdhd}((r2\_analoaf~X0~X7~X2~X8~X4){\unicdcdcdhd}\\
(r2\_aff\_1~X0~X3~X4~X6))))))))){\unicdcdcdid}(((\preoh (X5 \in X6){\unicdcdcdhd}(X5=X4)){\unicdcdcdhd}(\preoh (\preoh X5 \in \\
X6){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X8 .  \\
(m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdcdcdhd}((X7 \in X6){\unicdcdcdhd}((X8 \in X6){\unicdcdcdhd}((r2\_analoaf~\\
X0~X7~X1~X8~X5){\unicdcdcdhd}((r2\_analoaf~X0~X7~X2~X8~X4){\unicdcdcdhd}(r2\_aff\_1~X0~X5~X4~X6))))))))){\unicdcdcdid}\\
(X3=X5)))))))))))\end{array}$$
\end{theorem}
\end{document}
