\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{t48\_yellow\_9 (TMbAh3cja1Vkt7bsAXw864eA94b41bE6KmL)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_yellow\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_waybel11 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_pre\_topc : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m4\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_waybel\_9 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_waybel11 : {{\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 $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_orders\_2~X0~X1=g1\_orders\_2~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdcdcdhd}\\
(m4\_yellow\_6~X1~X0)){\unicdbdjdcd}((v1\_pre\_topc~(k13\_yellow\_6~X0~X1)){\unicdcdcdhd}(v2\_pre\_topc~\\
(k13\_yellow\_6~X0~X1)))\end{array}
\label{hyp:ggdgcdfdpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_orders\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_yellow\_9~X1~X0){\unicdbdjdcd}\\
(l1\_waybel\_9~X1))\end{array}
\label{hyp:egehpfngbdpfjhfgmgmgpghhpfjd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_waybel\_9}~{X0}})}{\unicdbdjdcd}{({{({{l1\_pre\_topc}~{X0}})}{\unicdcdcdhd}{({{l1\_orders\_2}~{X0}})}})}}}\label{hyp:egehpfmgbdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}(m4\_yellow\_6~(k2\_waybel11~X0)~X0)\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgbdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdcdcdhd}\\
(m4\_yellow\_6~X1~X0)){\unicdbdjdcd}((v1\_pre\_topc~(k13\_yellow\_6~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~\\
(k13\_yellow\_6~X0~X1)))\end{array}
\label{hyp:egehpflgbdddpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_waybel\_9~X1){\unicdbdjdcd}((\\
m1\_yellow\_9~X1~X0){\unicdbdjded}(g1\_orders\_2~(u1\_struct\_0~X1)~(u1\_orders\_2~\\
X1)=g1\_orders\_2~(u1\_struct\_0~X0)~(u1\_orders\_2~X0))))\end{array}
\label{hyp:egedpfjhfgmgmgpghhpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m4\_yellow\_6~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_pre\_topc~X2){\unicdcdcdhd}(l1\_pre\_topc~\\
X2)){\unicdbdjdcd}((X2=k13\_yellow\_6~X0~X1){\unicdbdjded}((u1\_struct\_0~X2=u1\_struct\_0~\\
X0){\unicdcdcdhd}(u1\_pre\_topc~X2=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))~({\uniddcgcg} X3 : \iota .  {\unicdcdadad} X4 .  (\\
m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((X4 \in X3){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~\\
X5){\unicdcdcdhd}((v4\_orders\_2~X5){\unicdcdcdhd}((v7\_waybel\_0~X5){\unicdcdcdhd}(l1\_waybel\_0~X5~X0)))){\unicdbdjdcd}\\
((k4\_tarski~X5~X4 \in X1){\unicdbdjdcd}(r1\_waybel\_0~X0~X5~X3)))))~({\uniddcgcg} X3 : \iota .  \\
X3))))))\end{array}
\label{hyp:egcdedpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v2\_pre\_topc~X0){\unicdbdjded}((u1\_struct\_0~\\
X0 \in u1\_pre\_topc~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((r1\_tarski~X1~(u1\_pre\_topc~\\
X0)){\unicdbdjdcd}(k5\_setfam\_1~(u1\_struct\_0~X0)~X1 \in u1\_pre\_topc~X0))){\unicdcdcdhd}({\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}(((X1 \in u1\_pre\_topc~\\
X0){\unicdcdcdhd}(X2 \in u1\_pre\_topc~X0)){\unicdbdjdcd}(k9\_subset\_1~(u1\_struct\_0~X0)~X1~X2 \in \\
u1\_pre\_topc~X0)))))))\end{array}
\label{hyp:egbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}(k5\_waybel11~X0=u1\_pre\_topc~(k13\_yellow\_6~X0~(k2\_waybel11~\\
X0)))\end{array}
\label{hyp:egbdcdpfhhbgjhcgfgmgbdbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfjhfgmgmgpghhpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_yellow\_9~X1~X0){\unicdbdjdcd}((u1\_pre\_topc~X1=k5\_waybel11~\\
X0){\unicdbdjdcd}(v2\_pre\_topc~X1)))\end{array}$$
\end{theorem}
\end{document}
