\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{t9\_poset\_1 (TMVKjyTECR8mE6YMBvmdH9JkvbTz5HNpYLF)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_poset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_orders\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v5\_orders\_3~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
((X1=k1\_yellow\_0~X0~(k2\_poset\_1~X0~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_abian~(u1\_struct\_0~X0)~X3~X2){\unicdbdjdcd}(r3\_orders\_2~\\
X0~X1~X3))))))\end{array}
\label{hyp:mgcdgdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v5\_orders\_3~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
(((v2\_poset\_1~X2~X0~X0){\unicdcdcdhd}(X1=k1\_yellow\_0~X0~(k2\_poset\_1~X0~X2))){\unicdbdjdcd}\\
(r2\_abian~(u1\_struct\_0~X0)~X1~X2))))\end{array}
\label{hyp:mgcdfdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_yellow\_0~\\
X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v5\_orders\_3~X1~X0~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}((v2\_poset\_1~X1~X0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((X2=k3\_poset\_1~X0~X1){\unicdbdjded}((r2\_abian~(u1\_struct\_0~\\
X0)~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_abian~\\
(u1\_struct\_0~X0)~X3~X1){\unicdbdjdcd}(r3\_orders\_2~X0~X2~X3))))))))\end{array}
\label{hyp:egfdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}\\
((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))))))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_orders\_2~\\
X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
((v1\_poset\_1~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))){\unicdbdjdcd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(v2\_poset\_1~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(v5\_orders\_3~X2~X0~X1)))))\end{array}
\label{hyp:dgdgcdpfahpgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfahpgdhfgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~X1~X0~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}(k3\_poset\_1~X0~X1=k1\_yellow\_0~X0~(k2\_poset\_1~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
