\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{t31\_fintopo6 (TMZSoaYxTLDoCkRPuQFuxHug44qHahBizvQ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_fin\_topo : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_fin\_topo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_fintopo6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_fintopo4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v4\_fin\_topo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_fin\_topo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_fin\_topo~\\
X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(\preoh (X1=k4\_subset\_1~(u1\_struct\_0~X0)~X2~X3){\unicdcdcdhd}((r1\_xboole\_0~X2~X3){\unicdcdcdhd}\\
((r1\_fintopo4~X0~X2~X3){\unicdcdcdhd}((X2{\unicdcdgdad}k1\_struct\_0~X0){\unicdcdcdhd}(X3{\unicdcdgdad}k1\_struct\_0~\\
X0)))))))){\unicdbdjdcd}(v4\_fin\_topo~X1~X0)))\end{array}
\label{hyp:ehhdpfggjgogehpgahpggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v3\_orders\_2~\\
X0){\unicdcdcdhd}((k2\_struct\_0~X0=k4\_subset\_1~(u1\_struct\_0~X0)~X1~X2){\unicdcdcdhd}(r1\_fintopo4~\\
X0~X1~X2))){\unicdbdjdcd}((v2\_fin\_topo~X1~X0){\unicdcdcdhd}(v3\_fin\_topo~X1~X0)))))\end{array}
\label{hyp:ehcdidpfggjgogehpgahpggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))){\unicdbdjdcd}((r1\_fintopo4~X0~X1~X2){\unicdbdjdcd}\\
(r1\_fintopo4~X0~X2~X1))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfggjgogehpgahpged}
\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 .  (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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v1\_fintopo6~\\
X0){\unicdbdjded}(v4\_fin\_topo~(k2\_struct\_0~X0)~X0))\end{array}
\label{hyp:egbdpfggjgogehpgahpggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k4\_subset\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfggjgogehpgahpggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}(((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_fin\_topo~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(\preoh (k2\_struct\_0~X0=k4\_subset\_1~(u1\_struct\_0~\\
X0)~X1~X2){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_struct\_0~X0){\unicdcdcdhd}((X2{\unicdcdgdad}k1\_struct\_0~X0){\unicdcdcdhd}((v3\_fin\_topo~\\
X1~X0){\unicdcdcdhd}((v3\_fin\_topo~X2~X0){\unicdcdcdhd}(r1\_xboole\_0~X1~X2)))))))))){\unicdbdjdcd}(v1\_fintopo6~\\
X0))\end{array}$$
\end{theorem}
\end{document}
