\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{l20\_topgen\_3 (TMNignRnNwkmJHDSzEfQu4MqpsKgqFTmhjK)}
\maketitle
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ c1\_\_topgen\_3 : {\iota}$ be given.
Let $ k2\_topgen\_3 : {\iota}$ be given.
Let $ v1\_cantor\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_cantor\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_rat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
((u1\_pre\_topc~X0=k1\_cantor\_1~(u1\_struct\_0~X0)~X1){\unicdbdjded}((v1\_tops\_2~\\
X1~X0){\unicdcdcdhd}((v1\_cantor\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:ehcdcdpfjhfgmgmgpghhpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}c1\_\_topgen\_3=ReplSep2~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~k1\_numbers))~\\
({\uniddcgcg} X0 : \iota .  toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k1\_numbers))~(\\
{\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  (\preoh r1\_xxreal\_0~X1~X0){\unicdcdcdhd}(v1\_rat\_1~X1))~(\\
{\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  k3\_rcomp\_1~X0~X1)\end{array}
\label{hyp:mgbdidpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_pre\_topc}~{k2\_topgen\_3}}={{{k1\_cantor\_1}~{k1\_numbers}}~{c1\_\_topgen\_3}}}\label{hyp:mgbdhdpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(k1\_zfmisc\_1~k1\_numbers))){\unicdcdcdhd}\\
((u1\_pre\_topc~k2\_topgen\_3=k1\_cantor\_1~k1\_numbers~X0){\unicdcdcdhd}(X0=ReplSep2~\\
(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k1\_numbers))~({\uniddcgcg} X1 : \iota .  \\
toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k1\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  (\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(v1\_rat\_1~X2))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  k3\_rcomp\_1~X1~X2)))\end{array}
\label{hyp:mgbdgdpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k2\_topgen\_3}}={k1\_numbers}}\label{hyp:mgbdfdpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k2\_topgen\_3){\unicdcdcdhd}((v1\_pre\_topc~k2\_topgen\_3){\unicdcdcdhd}((v2\_pre\_topc~\\
k2\_topgen\_3){\unicdcdcdhd}(l1\_pre\_topc~k2\_topgen\_3)))\end{array}
\label{hyp:egehpflgcdpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{c1\_\_topgen\_3}}~{({{k1\_zfmisc\_1}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}})}}\label{hyp:egehpfdgbdpfpfehpgahhgfgogpfdd}
\end{equation}
\begin{theorem}\label{thm:mgcdadpfehpgahhgfgogpfdd}
$$\begin{array}{c}(v1\_tops\_2~c1\_\_topgen\_3~k2\_topgen\_3){\unicdcdcdhd}((v1\_cantor\_1~c1\_\_topgen\_3~\\
k2\_topgen\_3){\unicdcdcdhd}(m1\_subset\_1~c1\_\_topgen\_3~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~k2\_topgen\_3)))))\end{array}$$
\end{theorem}
\end{document}
