\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\_waybel25 (TMQDKWTg7jF4g4TdG5saLoiEpMmgCTqJZHo)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_waybel25 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k3\_waybel24 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_waybel25 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ 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 $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_yellow\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_waybel\_9 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_9 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k6\_yellow\_1~X0~X1))){\unicdbdjded}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~X1)))))))\end{array}
\label{hyp:ehbdjdpfhhbgjhcgfgmgcded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~\\
X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(u1\_struct\_0~\\
X1)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k6\_yellow\_1~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k6\_yellow\_1~\\
X0~X1))){\unicdbdjdcd}(((X4=X2){\unicdcdcdhd}(X5=X3)){\unicdbdjdcd}((r1\_orders\_2~(k6\_yellow\_1~X0~X1)~\\
X4~X5){\unicdbdjded}(r1\_yellow\_2~X0~X1~X2~X3)))))))\end{array}
\label{hyp:ehbdbdpfhhbgjhcgfgmgbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k1\_waybel25~X0)){\unicdcdcdhd}(v1\_waybel\_9~(k1\_waybel25~X0)))\end{array}
\label{hyp:ggdgedpfhhbgjhcgfgmgcdfd}
\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 .  {\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}((v1\_orders\_2~(k6\_yellow\_1~\\
X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k6\_yellow\_1~X0~X1)))\end{array}
\label{hyp:egehpflggdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_waybel\_9~(k1\_waybel25~X0)){\unicdcdcdhd}\\
(l1\_waybel\_9~(k1\_waybel25~X0)))\end{array}
\label{hyp:egehpflgbdpfhhbgjhcgfgmgcdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_yellow\_0~X0~X1){\unicdbdjdcd}((X2=k1\_yellow\_0~X0~\\
X1){\unicdbdjded}((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:egjdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_lattice3~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(r1\_orders\_2~X0~X3~X2)))))\end{array}
\label{hyp:egjdpfmgbgehehjgdgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfhhbgjhcgfgmgcdfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}((v6\_pre\_topc~\\
X1){\unicdcdcdhd}((v1\_waybel25~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh \\
v2\_struct\_0~X2){\unicdcdcdhd}((v4\_orders\_2~X2){\unicdcdcdhd}((v7\_waybel\_0~X2){\unicdcdcdhd}(l1\_waybel\_0~\\
X2~(k3\_waybel24~X0~(k1\_waybel25~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~(k1\_waybel25~\\
X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~(k1\_waybel25~X1))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~(k1\_waybel25~\\
X1))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~(k1\_waybel25~X1))))))){\unicdbdjdcd}(((X3=k1\_yellow\_0~(\\
k6\_yellow\_1~(u1\_struct\_0~X0)~(k1\_waybel25~X1))~(k2\_relset\_1~(\\
u1\_struct\_0~(k3\_waybel24~X0~(k1\_waybel25~X1)))~(u1\_waybel\_0~(\\
k3\_waybel24~X0~(k1\_waybel25~X1))~X2))){\unicdcdcdhd}((r1\_yellow\_0~(k6\_yellow\_1~\\
(u1\_struct\_0~X0)~(k1\_waybel25~X1))~(k2\_relset\_1~(u1\_struct\_0~\\
(k3\_waybel24~X0~(k1\_waybel25~X1)))~(u1\_waybel\_0~(k3\_waybel24~\\
X0~(k1\_waybel25~X1))~X2))){\unicdcdcdhd}(X4 \in k2\_relset\_1~(u1\_struct\_0~(k3\_waybel24~\\
X0~(k1\_waybel25~X1)))~(u1\_waybel\_0~(k3\_waybel24~X0~(k1\_waybel25~\\
X1))~X2)))){\unicdbdjdcd}(r1\_yellow\_2~(u1\_struct\_0~X0)~(k1\_waybel25~X1)~X4~\\
X3))))))\end{array}$$
\end{theorem}
\end{document}
