\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{l56\_poset\_1 (TMKU8z2Ef5x9Hia8xha9RUC7fKj5ZXT3Lqb)}
\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 $ k10\_poset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k6\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_orders\_3 : {{\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 $ v2\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 .  ((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}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
((r1\_yellow\_2~(u1\_struct\_0~X0)~X0~X1~X2){\unicdbdjdcd}(r3\_orders\_2~X0~(k3\_poset\_1~\\
X0~X1)~(k3\_poset\_1~X0~X2)))))\end{array}
\label{hyp:ehbdadpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}((r3\_orders\_2~X0~X1~X2){\unicdbdjded}(r1\_orders\_2~\\
X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchddpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\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~\\
(k6\_poset\_1~X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k6\_poset\_1~X0~X0))){\unicdbdjdcd}((r3\_orders\_2~(k6\_poset\_1~X0~X0)~X1~X2){\unicdbdjdcd}(\\
(X1 \in k4\_poset\_1~X0~X0){\unicdcdcdhd}((X2 \in k4\_poset\_1~X0~X0){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~\\
X3~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))){\unicdcdcdhd}({\unicdcdaddd} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~X4~X0~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}((X2=X4){\unicdcdcdhd}(r1\_yellow\_2~(u1\_struct\_0~X0)~\\
X0~X3~X4))))))))))\end{array}
\label{hyp:mgfdfdpfahpgdhfgehpfbd}
\end{equation}
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}((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}((\preoh v2\_struct\_0~(k6\_poset\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_orders\_2~(k6\_poset\_1~X0~X1)){\unicdcdcdhd}((v3\_orders\_2~(k6\_poset\_1~\\
X0~X1)){\unicdcdcdhd}((v4\_orders\_2~(k6\_poset\_1~X0~X1)){\unicdcdcdhd}((v5\_orders\_2~(k6\_poset\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_poset\_1~(k6\_poset\_1~X0~X1)))))))\end{array}
\label{hyp:ggdggdpfahpgdhfgehpfbd}
\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}((\preoh v2\_struct\_0~(k6\_poset\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_orders\_2~(k6\_poset\_1~X0~X1)){\unicdcdcdhd}((v3\_orders\_2~(k6\_poset\_1~\\
X0~X1)){\unicdcdcdhd}((v4\_orders\_2~(k6\_poset\_1~X0~X1)){\unicdcdcdhd}((v5\_orders\_2~(k6\_poset\_1~\\
X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k6\_poset\_1~X0~X1)))))))\end{array}
\label{hyp:egehpflggdpfahpgdhfgehpfbd}
\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}(m1\_subset\_1~(k5\_poset\_1~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_poset\_1~X0~X1)~(k4\_poset\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgfdpfahpgdhfgehpfbd}
\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}(\preoh v1\_xboole\_0~(k4\_poset\_1~\\
X0~X1))\end{array}
\label{hyp:egehpflgedpfahpgdhfgehpfbd}
\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}((v1\_funct\_1~(k10\_poset\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k10\_poset\_1~X0)~(u1\_struct\_0~(k6\_poset\_1~X0~X0))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k10\_poset\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k6\_poset\_1~X0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgbdadpfahpgdhfgehpfbd}
\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 .  ((\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}(k6\_poset\_1~X0~X1=g1\_orders\_2~\\
(k4\_poset\_1~X0~X1)~(k5\_poset\_1~X0~X1)))\end{array}
\label{hyp:egidpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((v5\_orders\_3~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_orders\_2~X0~X3~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}(((X5=k1\_funct\_1~X2~X3){\unicdcdcdhd}(X6=k1\_funct\_1~X2~X4)){\unicdbdjdcd}(r1\_orders\_2~\\
X1~X5~X6))))))))))\end{array}
\label{hyp:egfdpfpgchegfgchdhpfdd}
\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~(k6\_poset\_1~X0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k6\_poset\_1~X0~X0))~\\
(u1\_struct\_0~X0)))))){\unicdbdjdcd}((X1=k10\_poset\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k6\_poset\_1~X0~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~\\
X3~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~\\
(k6\_poset\_1~X0~X0))~(u1\_struct\_0~X0)~X1~X2=k3\_poset\_1~X0~X3))))))\end{array}
\label{hyp:egbdcdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~X0){\unicdbdjdcd}(X0=g1\_orders\_2~\\
(u1\_struct\_0~X0)~(u1\_orders\_2~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfpgchegfgchdhpfcd}
\end{equation}
\begin{theorem}\label{thm:mgfdgdpfahpgdhfgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}((v1\_funct\_1~(k10\_poset\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k10\_poset\_1~X0)~(u1\_struct\_0~(k6\_poset\_1~X0~X0))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v5\_orders\_3~(k10\_poset\_1~X0)~(k6\_poset\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
(k10\_poset\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k6\_poset\_1~\\
X0~X0))~(u1\_struct\_0~X0)))))))\end{array}$$
\end{theorem}
\end{document}
