\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{l24\_topalg\_5 (TMLjk2b4j8Gm88rzbXtSo1ama5ZfJ8UwMWJ)}
\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 $ v1\_tsep\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_connsp\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pre\_topc : {{\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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_connsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(m1\_subset\_1~(u1\_struct\_0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ehbdpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v1\_connsp\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((v3\_pre\_topc~X1~X0){\unicdbdjdcd}(v2\_connsp\_2~\\
X1~X0))))\end{array}
\label{hyp:ehbdhdpfdgpgogogdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v1\_connsp\_2~X0){\unicdbdjded}(v2\_connsp\_2~(k2\_struct\_0~X0)~X0))\end{array}
\label{hyp:ehbdddpfehpgahbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\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}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}(((g1\_pre\_topc~(u1\_struct\_0~X0)~(u1\_pre\_topc~X0)=g1\_pre\_topc~\\
(u1\_struct\_0~X1)~(u1\_pre\_topc~X1)){\unicdcdcdhd}(v1\_connsp\_2~X0)){\unicdbdjdcd}(v1\_connsp\_2~\\
X1)))\end{array}
\label{hyp:ehbdcdpfehpgahbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\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}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X1)))){\unicdbdjdcd}(((X2=X3){\unicdcdcdhd}(v2\_connsp\_2~\\
X2~X0)){\unicdbdjdcd}(v2\_connsp\_2~X3~X1)))))\end{array}
\label{hyp:ehbdbdpfehpgahbgmghgpffd}
\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~\\
(g1\_pre\_topc~(u1\_struct\_0~X0)~(u1\_pre\_topc~X0))){\unicdcdcdhd}(v1\_pre\_topc~\\
(g1\_pre\_topc~(u1\_struct\_0~X0)~(u1\_pre\_topc~X0))))\end{array}
\label{hyp:ggdghdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}((v1\_pre\_topc~\\
(g1\_pre\_topc~(u1\_struct\_0~X0)~(u1\_pre\_topc~X0))){\unicdcdcdhd}(v2\_pre\_topc~\\
(g1\_pre\_topc~(u1\_struct\_0~X0)~(u1\_pre\_topc~X0))))\end{array}
\label{hyp:ggdggdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_pre\_topc~X0)~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(l1\_pre\_topc~X1))\end{array}
\label{hyp:egehpfngbdpfahchfgpfehpgahdg}
\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 .  (l1\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_struct\_0~X0)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}((v1\_pre\_topc~(g1\_pre\_topc~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(g1\_pre\_topc~\\
X0~X1)))\end{array}
\label{hyp:egehpfhgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k2\_struct\_0}~{X0}}={{u1\_struct\_0}~{X0}}})}}}\label{hyp:egddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
((v1\_tsep\_1~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
u1\_struct\_0~X0))){\unicdbdjdcd}((X2=u1\_struct\_0~X1){\unicdbdjdcd}(v3\_pre\_topc~X2~X0)))))\end{array}
\label{hyp:egbdpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_pre\_topc~X1~X0){\unicdbdjdcd}(v2\_pre\_topc~X1))\end{array}
\label{hyp:dgdgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_pre\_topc~X0){\unicdbdjdcd}(X0=g1\_pre\_topc~\\
(u1\_struct\_0~X0)~(u1\_pre\_topc~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:mgcdedpfehpgahbgmghgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_tsep\_1~X1~X0){\unicdcdcdhd}(m1\_pre\_topc~\\
X1~X0))){\unicdbdjdcd}((v1\_connsp\_2~X0){\unicdbdjdcd}(v1\_connsp\_2~(g1\_pre\_topc~(u1\_struct\_0~\\
X1)~(u1\_pre\_topc~X1)))))\end{array}$$
\end{theorem}
\end{document}
