\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{t40\_waybel\_9 (TMZyd1kjNarBwn98UU16JHZJ4yk2sSogfQQ)}
\maketitle
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_pre\_topc : {{\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\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compts\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_9 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\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 $ v11\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_waybel\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_waybel\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v10\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_waybel\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_waybel\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_waybel\_9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_waybel\_9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v9\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\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 $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (k9\_xtuple\_0~(k4\_relat\_1~X0)=X0){\unicdcdcdhd}(k10\_xtuple\_0~(\\
k4\_relat\_1~X0)=X0)\end{array}
\label{hyp:ehedfdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v8\_pre\_topc~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}\\
((v2\_lattice3~X0){\unicdcdcdhd}((v1\_compts\_1~X0){\unicdcdcdhd}(l1\_waybel\_9~X0))))))))){\unicdbdjdcd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v5\_pre\_topc~\\
(k4\_waybel\_1~X0~X1)~X0~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}((\\
v11\_waybel\_0~X1~X0){\unicdbdjdcd}((r2\_waybel\_9~X0~X1){\unicdcdcdhd}(k1\_waybel\_9~X0~X1 \in k10\_yellow\_6~\\
X0~X1)))))\end{array}
\label{hyp:ehddjdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v8\_pre\_topc~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}\\
((v2\_lattice3~X0){\unicdcdcdhd}((v1\_compts\_1~X0){\unicdcdcdhd}(l1\_waybel\_9~X0))))))))){\unicdbdjdcd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v5\_pre\_topc~\\
(k4\_waybel\_1~X0~X1)~X0~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}((\\
v10\_waybel\_0~X1~X0){\unicdbdjdcd}((r1\_waybel\_9~X0~X1){\unicdcdcdhd}(k1\_waybel\_2~X0~X1 \in k10\_yellow\_6~\\
X0~X1)))))\end{array}
\label{hyp:ehddidpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (((X1=k2\_yellow\_0~\\
X0~X2){\unicdcdcdhd}(r2\_yellow\_0~X0~X2)){\unicdbdjdcd}((r1\_lattice3~X0~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_lattice3~X0~X2~X3){\unicdbdjdcd}(r1\_orders\_2~\\
X0~X3~X1))))){\unicdcdcdhd}(((r1\_lattice3~X0~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_lattice3~X0~X2~X3){\unicdbdjdcd}(r1\_orders\_2~X0~X3~\\
X1)))){\unicdbdjdcd}((X1=k2\_yellow\_0~X0~X2){\unicdcdcdhd}(r2\_yellow\_0~X0~X2)))))\end{array}
\label{hyp:ehddbdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (((X1=k1\_yellow\_0~\\
X0~X2){\unicdcdcdhd}(r1\_yellow\_0~X0~X2)){\unicdbdjdcd}((r2\_lattice3~X0~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_lattice3~X0~X2~X3){\unicdbdjdcd}(r1\_orders\_2~\\
X0~X1~X3))))){\unicdcdcdhd}(((r2\_lattice3~X0~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_lattice3~X0~X2~X3){\unicdbdjdcd}(r1\_orders\_2~X0~X1~\\
X3)))){\unicdbdjdcd}((X1=k1\_yellow\_0~X0~X2){\unicdcdcdhd}(r1\_yellow\_0~X0~X2)))))\end{array}
\label{hyp:ehddadpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k2\_relset\_1~X0~X1=k10\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k2\_waybel\_9~X0)){\unicdcdcdhd}(v6\_waybel\_0~(k2\_waybel\_9~X0)~X0))\end{array}
\label{hyp:ggdgjdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v6\_waybel\_0~\\
(k3\_waybel\_9~X0)~X0){\unicdcdcdhd}((v9\_waybel\_0~(k3\_waybel\_9~X0)~X0){\unicdcdcdhd}(v11\_waybel\_0~\\
(k3\_waybel\_9~X0)~X0)))\end{array}
\label{hyp:ggdgcdbdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v6\_waybel\_0~\\
(k3\_waybel\_9~X0)~X0){\unicdcdcdhd}(v7\_waybel\_0~(k3\_waybel\_9~X0)))\end{array}
\label{hyp:ggdgcdadpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v4\_orders\_2~\\
(k3\_waybel\_9~X0)){\unicdcdcdhd}(v6\_waybel\_0~(k3\_waybel\_9~X0)~X0))\end{array}
\label{hyp:ggdgbdjdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k3\_waybel\_9~X0)){\unicdcdcdhd}(v6\_waybel\_0~(k3\_waybel\_9~X0)~X0))\end{array}
\label{hyp:ggdgbdgdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v6\_waybel\_0~\\
(k2\_waybel\_9~X0)~X0){\unicdcdcdhd}((v8\_waybel\_0~(k2\_waybel\_9~X0)~X0){\unicdcdcdhd}(v10\_waybel\_0~\\
(k2\_waybel\_9~X0)~X0)))\end{array}
\label{hyp:ggdgbdfdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v6\_waybel\_0~\\
(k2\_waybel\_9~X0)~X0){\unicdcdcdhd}(v7\_waybel\_0~(k2\_waybel\_9~X0)))\end{array}
\label{hyp:ggdgbdddpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v4\_orders\_2~\\
(k2\_waybel\_9~X0)){\unicdcdcdhd}(v6\_waybel\_0~(k2\_waybel\_9~X0)~X0))\end{array}
\label{hyp:ggdgbdcdpfhhbgjhcgfgmgpfjd}
\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\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_partfun1~(k6\_partfun1~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k6\_partfun1~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))\end{array}
\label{hyp:egehpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}}\label{hyp:egehpflgedpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v6\_waybel\_0~(k3\_waybel\_9~X0)~X0){\unicdcdcdhd}\\
(l1\_waybel\_0~(k3\_waybel\_9~X0)~X0))\end{array}
\label{hyp:egehpflgddpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_yellow\_0~\\
X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v6\_waybel\_0~(k2\_waybel\_9~X0)~X0){\unicdcdcdhd}\\
(l1\_waybel\_0~(k2\_waybel\_9~X0)~X0))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgpfjd}
\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 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v6\_waybel\_0~X1~X0){\unicdcdcdhd}\\
(l1\_waybel\_0~X1~X0)){\unicdbdjdcd}((X1=k3\_waybel\_9~X0){\unicdbdjded}((u1\_struct\_0~X1=\\
u1\_struct\_0~X0){\unicdcdcdhd}((u1\_orders\_2~X1=k3\_relset\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)~(u1\_orders\_2~X0)){\unicdcdcdhd}(u1\_waybel\_0~X0~X1=k3\_struct\_0~\\
X0)))))\end{array}
\label{hyp:eggdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v2\_yellow\_0~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(r2\_lattice3~X0~(u1\_struct\_0~\\
X0)~X1)))\end{array}
\label{hyp:egfdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v6\_waybel\_0~X1~X0){\unicdcdcdhd}\\
(l1\_waybel\_0~X1~X0)){\unicdbdjdcd}((X1=k2\_waybel\_9~X0){\unicdbdjded}((g1\_orders\_2~(u1\_struct\_0~\\
X1)~(u1\_orders\_2~X1)=g1\_orders\_2~(u1\_struct\_0~X0)~(u1\_orders\_2~\\
X0)){\unicdcdcdhd}(u1\_waybel\_0~X0~X1=k3\_struct\_0~X0))))\end{array}
\label{hyp:egfdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_yellow\_0~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(r1\_lattice3~X0~(u1\_struct\_0~\\
X0)~X1)))\end{array}
\label{hyp:egedpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_waybel\_0~X1~X0){\unicdbdjdcd}\\
((r2\_waybel\_9~X0~X1){\unicdbdjded}(r2\_yellow\_0~X0~(k2\_relset\_1~(u1\_struct\_0~\\
X0)~(u1\_waybel\_0~X0~X1)))))\end{array}
\label{hyp:egedpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}(k3\_struct\_0~X0=k6\_partfun1~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_waybel\_0~X1~X0){\unicdbdjdcd}\\
((r1\_waybel\_9~X0~X1){\unicdbdjded}(r1\_yellow\_0~X0~(k2\_relset\_1~(u1\_struct\_0~\\
X0)~(u1\_waybel\_0~X0~X1)))))\end{array}
\label{hyp:egddpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((v1\_yellow\_0~X0){\unicdcdcdhd}(v2\_yellow\_0~\\
X0)){\unicdbdjdcd}(v3\_yellow\_0~X0))\end{array}
\label{hyp:dgdgfdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v1\_lattice3}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgbdpfmgbgehehjgdgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfhhbgjhcgfgmgpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v8\_pre\_topc~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}\\
((v2\_lattice3~X0){\unicdcdcdhd}((v1\_compts\_1~X0){\unicdcdcdhd}(l1\_waybel\_9~X0))))))))){\unicdbdjdcd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v5\_pre\_topc~\\
(k4\_waybel\_1~X0~X1)~X0~X0)){\unicdbdjdcd}(v3\_yellow\_0~X0))\end{array}$$
\end{theorem}
\end{document}
