\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{t17\_yellow19 (TMLqzt7mwht6eLQxuc8GrWhTQ9yqLWLcFqS)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v13\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\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 $ k10\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_yellow19 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_waybel\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow19 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_waybel\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_subset\_1~X1~(u1\_struct\_0~(k3\_yellow\_1~\\
(k2\_struct\_0~X0)))){\unicdcdcdhd}((v2\_waybel\_0~X1~(k3\_yellow\_1~(k2\_struct\_0~\\
X0))){\unicdcdcdhd}((v13\_waybel\_0~X1~(k3\_yellow\_1~(k2\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_1~(k2\_struct\_0~X0))))))))){\unicdbdjdcd}\\
(X1=k2\_yellow19~X0~(k3\_yellow19~X0~(k2\_struct\_0~X0)~X1)))\end{array}
\label{hyp:ehbdedpfjhfgmgmgpghhbdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v7\_waybel\_0~\\
X1){\unicdcdcdhd}(l1\_waybel\_0~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((X2 \in k10\_yellow\_6~X0~X1){\unicdbdjded}(r2\_waybel\_7~X0~(k2\_yellow19~X0~\\
X1)~X2))))\end{array}
\label{hyp:ehbdcdpfjhfgmgmgpghhbdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~\\
X0)){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_subset\_1~X2~(u1\_struct\_0~(k3\_yellow\_1~\\
X1))){\unicdcdcdhd}((v2\_waybel\_0~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}((v13\_waybel\_0~X2~(\\
k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(\\
k3\_yellow\_1~X1)))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k3\_yellow19~X0~X1~X2)){\unicdcdcdhd}\\
((v6\_waybel\_0~(k3\_yellow19~X0~X1~X2)~X0){\unicdcdcdhd}(v7\_waybel\_0~(k3\_yellow19~\\
X0~X1~X2))))\end{array}
\label{hyp:ggdgfdpfjhfgmgmgpghhbdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k2\_struct\_0~X0))\end{array}
\label{hyp:ggdgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~\\
X0)){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v2\_waybel\_0~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}\\
((v13\_waybel\_0~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_1~X1))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k3\_yellow19~\\
X0~X1~X2)){\unicdcdcdhd}((v3\_orders\_2~(k3\_yellow19~X0~X1~X2)){\unicdcdcdhd}((v4\_orders\_2~\\
(k3\_yellow19~X0~X1~X2)){\unicdcdcdhd}(v6\_waybel\_0~(k3\_yellow19~X0~X1~X2)~X0))))\end{array}
\label{hyp:ggdgedpfjhfgmgmgpghhbdjd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~\\
X0)){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v2\_waybel\_0~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}\\
((v13\_waybel\_0~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_1~X1))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k3\_yellow19~\\
X0~X1~X2)){\unicdcdcdhd}((v6\_waybel\_0~(k3\_yellow19~X0~X1~X2)~X0){\unicdcdcdhd}(l1\_waybel\_0~\\
(k3\_yellow19~X0~X1~X2)~X0)))\end{array}
\label{hyp:egehpflgddpfjhfgmgmgpghhbdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_struct\_0~X0)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgcdpfdhehchfhdgehpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfjhfgmgmgpghhbdjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_subset\_1~X1~(u1\_struct\_0~\\
(k3\_yellow\_1~(k2\_struct\_0~X0)))){\unicdcdcdhd}((v2\_waybel\_0~X1~(k3\_yellow\_1~\\
(k2\_struct\_0~X0))){\unicdcdcdhd}((v13\_waybel\_0~X1~(k3\_yellow\_1~(k2\_struct\_0~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_1~\\
(k2\_struct\_0~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((X2 \in k10\_yellow\_6~X0~(k3\_yellow19~X0~(k2\_struct\_0~X0)~X1)){\unicdbdjded}\\
(r2\_waybel\_7~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
