\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{l4\_homothet (TMVP6tg6mHNG4dTPEzcYKyK6uW88Vjqo7qq)}
\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 $ v7\_aff\_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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r5\_aff\_1 : {{\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.
Let $ r3\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_aff\_2 : {{\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~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((r3\_aff\_1~X0~X1~X2){\unicdbdjdcd}((v1\_aff\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_1~X2~X0)))))\end{array}
\label{hyp:ehddgdpfbgggggpfbd}
\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}((v7\_aff\_2~X0){\unicdbdjdcd}(v11\_aff\_2~X0))\end{array}
\label{hyp:ehbdedpfbgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~\\
X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))){\unicdbdjdcd}((r5\_aff\_1~\\
X0~X1~X2){\unicdbdjded}(r3\_aff\_1~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchfdpfbgggggpfbd}
\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}\\
((v11\_aff\_2~X0){\unicdbdjded}({\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}(((r5\_aff\_1~X0~X1~X2){\unicdcdcdhd}((r5\_aff\_1~X0~X1~X3){\unicdcdcdhd}\\
((X4 \in X1){\unicdcdcdhd}((X7 \in X1){\unicdcdcdhd}((X5 \in X2){\unicdcdcdhd}((X8 \in X2){\unicdcdcdhd}((X6 \in X3){\unicdcdcdhd}((X9 \in X3){\unicdcdcdhd}(\\
(v1\_aff\_1~X1~X0){\unicdcdcdhd}((v1\_aff\_1~X2~X0){\unicdcdcdhd}((v1\_aff\_1~X3~X0){\unicdcdcdhd}((r2\_analoaf~\\
X0~X4~X5~X7~X8){\unicdcdcdhd}(r2\_analoaf~X0~X4~X6~X7~X9))))))))))))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}\\
((X1=X3){\unicdcdcdid}(r2\_analoaf~X0~X5~X6~X8~X9))))))))))))))\end{array}
\label{hyp:egbdbdpfbgggggpfcd}
\end{equation}
\begin{theorem}\label{thm:mgedpfigpgngpgehigfgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_diraf~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0)))){\unicdbdjdcd}((v7\_aff\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(((r5\_aff\_1~X0~X1~X2){\unicdcdcdhd}((r5\_aff\_1~X0~X1~X3){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}((X5 \in X1){\unicdcdcdhd}\\
((X6 \in X2){\unicdcdcdhd}((X7 \in X2){\unicdcdcdhd}((X8 \in X3){\unicdcdcdhd}((X9 \in X3){\unicdcdcdhd}((r2\_analoaf~X0~X4~X6~X5~\\
X7){\unicdcdcdhd}(r2\_analoaf~X0~X4~X8~X5~X9)))))))))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}((X1=X3){\unicdcdcdid}(\\
r2\_analoaf~X0~X6~X8~X7~X9))))))))))))))\end{array}$$
\end{theorem}
\end{document}
