\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{t21\_waybel24 (TMSjQm8o5kJ7yTXsJNFftQcdWes2gVY87gG)}
\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 $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_9 : {{\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 $ v5\_pre\_topc : {{\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\_waybel24 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v13\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_yellow\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}((v12\_waybel\_0~X1~X0){\unicdcdcdhd}(v13\_waybel\_0~X1~X0))))\end{array}
\label{hyp:chdgidpfhhbgjhcgfgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_waybel\_9~\\
X1)))){\unicdbdjdcd}((v1\_monoid\_0~(k3\_waybel24~X0~X1)){\unicdcdcdhd}(v1\_orders\_2~(k3\_waybel24~\\
X0~X1)))\end{array}
\label{hyp:ggdghdpfhhbgjhcgfgmgcded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_waybel\_9~\\
X1)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k3\_waybel24~X0~X1)){\unicdcdcdhd}(v1\_orders\_2~(k3\_waybel24~\\
X0~X1)))\end{array}
\label{hyp:ggdggdpfhhbgjhcgfgmgcded}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_pre\_topc~X0){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_waybel\_9~X1))){\unicdbdjdcd}((v1\_orders\_2~(k3\_waybel24~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~\\
(k3\_waybel24~X0~X1)))\end{array}
\label{hyp:egehpflgddpfhhbgjhcgfgmgcded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_waybel\_9~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~\\
X2)){\unicdbdjdcd}((X2=k3\_waybel24~X0~X1){\unicdbdjded}(((v4\_yellow\_0~X2~(k6\_yellow\_1~\\
(u1\_struct\_0~X0)~X1)){\unicdcdcdhd}(m1\_yellow\_0~X2~(k6\_yellow\_1~(u1\_struct\_0~\\
X0)~X1))){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in u1\_struct\_0~X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}\\
((X3=X4){\unicdcdcdhd}(v5\_pre\_topc~X4~X0~X1))))))))\end{array}
\label{hyp:egddpfhhbgjhcgfgmgcded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_monoid\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~\\
X1)))\end{array}
\label{hyp:dgdgbdpfngpgogpgjgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfhhbgjhcgfgmgcded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}((v3\_orders\_2~\\
X1){\unicdcdcdhd}(l1\_waybel\_9~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v5\_pre\_topc~X2~X0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))))))){\unicdbdjded}(m1\_subset\_1~X2~(u1\_struct\_0~(k3\_waybel24~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
