\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{t38\_waybel\_9 (TMXRCAC5vyZhceqGQ6QnqrsmyaaQv3oX83Y)}
\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 $ 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 $ 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 $ k10\_yellow\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_waybel\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}({\unicdcdadad} X2 .  ((\\
\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v4\_orders\_2~X2){\unicdcdcdhd}((v7\_waybel\_0~X2){\unicdcdcdhd}(l1\_waybel\_0~\\
X2~X0)))){\unicdbdjdcd}((({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(v5\_pre\_topc~\\
(k4\_waybel\_1~X0~X3)~X0~X0)){\unicdcdcdhd}((v10\_waybel\_0~X2~X0){\unicdcdcdhd}(r3\_waybel\_9~\\
X0~X2~X1))){\unicdbdjdcd}(X1=k1\_waybel\_2~X0~X2))))\end{array}
\label{hyp:ehddfdpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v8\_pre\_topc~\\
X0){\unicdcdcdhd}((v1\_compts\_1~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}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r3\_waybel\_9~X0~X1~X2){\unicdcdcdhd}(r3\_waybel\_9~\\
X0~X1~X3)){\unicdbdjdcd}(X2=X3)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r3\_waybel\_9~X0~X1~X2){\unicdbdjdcd}(X2 \in k10\_yellow\_6~X0~X1)))))\end{array}
\label{hyp:ehddddpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v8\_pre\_topc~\\
X0){\unicdcdcdhd}((v1\_compts\_1~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}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(r3\_waybel\_9~\\
X0~X1~X2)))\end{array}
\label{hyp:ehddadpfhhbgjhcgfgmgpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(r1\_yellow\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((r2\_lattice3~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r2\_lattice3~X0~X1~X3){\unicdbdjdcd}(r1\_orders\_2~X0~X2~X3))))))\end{array}
\label{hyp:ehbdfdpfjhfgmgmgpghhpfad}
\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 .  ((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 .  ((\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(((X2=X3){\unicdcdcdhd}\\
(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(v5\_pre\_topc~\\
(k4\_waybel\_1~X0~X4)~X0~X0)){\unicdcdcdhd}(r3\_waybel\_9~X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_lattice3~X0~(k2\_relset\_1~\\
(u1\_struct\_0~X0)~(u1\_waybel\_0~X0~X1))~X4){\unicdbdjdcd}(r3\_orders\_2~X0~X3~X4)))))))\end{array}
\label{hyp:mgedjdpfhhbgjhcgfgmgpfjd}
\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 .  ((\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(((X2=X3){\unicdcdcdhd}\\
(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(v5\_pre\_topc~\\
(k4\_waybel\_1~X0~X4)~X0~X0)){\unicdcdcdhd}((v10\_waybel\_0~X1~X0){\unicdcdcdhd}(r3\_waybel\_9~\\
X0~X1~X2)))){\unicdbdjdcd}(r2\_lattice3~X0~(k2\_relset\_1~(u1\_struct\_0~X0)~(u1\_waybel\_0~\\
X0~X1))~X3)))))\end{array}
\label{hyp:mgedidpfhhbgjhcgfgmgpfjd}
\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}
\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}
{{\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:ehddidpfhhbgjhcgfgmgpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}((v8\_pre\_topc~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}\\
((v2\_lattice3~X0){\unicdcdcdhd}((v1\_compts\_1~X0){\unicdcdcdhd}(l1\_waybel\_9~X0))))))))){\unicdbdjdcd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v5\_pre\_topc~\\
(k4\_waybel\_1~X0~X1)~X0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\\
v4\_orders\_2~X1){\unicdcdcdhd}((v7\_waybel\_0~X1){\unicdcdcdhd}(l1\_waybel\_0~X1~X0)))){\unicdbdjdcd}((\\
v10\_waybel\_0~X1~X0){\unicdbdjdcd}((r1\_waybel\_9~X0~X1){\unicdcdcdhd}(k1\_waybel\_2~X0~X1 \in k10\_yellow\_6~\\
X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
