\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{l17\_homothet (TMZPPeCoRiumvPj4ScGxRqx737pnSo9K18M)}
\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 $ v4\_aff\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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}((r2\_analoaf~\\
X0~X1~X2~X3~X4){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X4~X3){\unicdcdcdhd}((r2\_analoaf~X0~X2~X1~X3~\\
X4){\unicdcdcdhd}((r2\_analoaf~X0~X2~X1~X4~X3){\unicdcdcdhd}((r2\_analoaf~X0~X3~X4~X1~X2){\unicdcdcdhd}((r2\_analoaf~\\
X0~X3~X4~X2~X1){\unicdcdcdhd}((r2\_analoaf~X0~X4~X3~X1~X2){\unicdcdcdhd}(r2\_analoaf~X0~X4~X3~X2~\\
X1))))))))))))\end{array}
\label{hyp:ehedpfbgggggpfbd}
\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}(((v4\_aff\_2~X0){\unicdcdcdhd}((r1\_aff\_1~X0~X1~X2~X3){\unicdcdcdhd}(\\
(r1\_aff\_1~X0~X1~X4~X5){\unicdcdcdhd}((r2\_analoaf~X0~X2~X4~X3~X5){\unicdcdcdhd}(r1\_aff\_1~X0~X1~\\
X2~X6))))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}((r1\_aff\_1~X0~X1~X2~X4){\unicdcdcdid}(({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (\preoh r1\_aff\_1~X0~X1~X2~X8){\unicdcdcdhd}((r1\_aff\_1~X0~X1~X8~X9){\unicdcdcdhd}((r2\_analoaf~\\
X0~X2~X8~X3~X9){\unicdcdcdhd}((r2\_analoaf~X0~X8~X6~X9~X7){\unicdcdcdhd}(r1\_aff\_1~X0~X1~X2~X7))))))){\unicdcdcdid}\\
(r2\_analoaf~X0~X4~X6~X5~X7))))))))))))\end{array}
\label{hyp:mgbdgdpfigpgngpgehigfgeh}
\end{equation}
\begin{theorem}\label{thm:mgbdhdpfigpgngpgehigfgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_diraf~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~X0)){\unicdbdjdcd}(((v4\_aff\_2~X0){\unicdcdcdhd}((r1\_aff\_1~X0~X1~X2~X3){\unicdcdcdhd}(\\
(r1\_aff\_1~X0~X1~X2~X4){\unicdcdcdhd}((r1\_aff\_1~X0~X1~X6~X7){\unicdcdcdhd}(r2\_analoaf~X0~X2~X6~\\
X3~X7))))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_aff\_1~\\
X0~X1~X2~X8){\unicdcdcdhd}((r1\_aff\_1~X0~X1~X8~X9){\unicdcdcdhd}((r2\_analoaf~X0~X2~X8~X3~X9){\unicdcdcdhd}(\\
(r2\_analoaf~X0~X8~X4~X9~X5){\unicdcdcdhd}(r1\_aff\_1~X0~X1~X2~X5))))))){\unicdcdcdid}((r1\_aff\_1~\\
X0~X1~X2~X6){\unicdcdcdid}(r2\_analoaf~X0~X4~X6~X5~X7))))))))))))\end{array}$$
\end{theorem}
\end{document}
