\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{t55\_topgen\_5 (TMcuaNt3aqXWSnfBDZHfsXvMxwzXjkCQhTs)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_topgen\_3 : {\iota}$ 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 $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ k3\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_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 $ 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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k6\_subset\_1~\\
(k4\_xxreal\_1~k2\_xxreal\_0~X0)~(k3\_xxreal\_1~k2\_xxreal\_0~X1)=k4\_xxreal\_1~\\
X1~X0))\end{array}
\label{hyp:ehcdididpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_numbers}={{{k4\_xxreal\_1}~{k2\_xxreal\_0}}~{k1\_xxreal\_0}}}\label{hyp:ehcdcdedpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v3\_pre\_topc~(k3\_limfunc1~X0)~k2\_topgen\_3){\unicdcdcdhd}\\
(m1\_subset\_1~(k3\_limfunc1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~k2\_topgen\_3))))\end{array}
\label{hyp:ehbdedpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k3\_subset\_1~\\
X0~(k3\_subset\_1~X0~X1)=X1)\end{array}
\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgddpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v3\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}(v4\_pre\_topc~(k3\_subset\_1~(u1\_struct\_0~X0)~X1)~X0)\end{array}
\label{hyp:ggdgddpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgbdpfihihchfgbgmgpfad}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_limfunc1~X0)~(k1\_zfmisc\_1~\\
k1\_numbers))\end{array}
\label{hyp:egehpflgbdpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(k3\_subset\_1~\\
X0~X1=k4\_xboole\_0~X0~X1)\end{array}
\label{hyp:egedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k3\_limfunc1~X0=k4\_xxreal\_1~X0~k1\_xxreal\_0)\end{array}
\label{hyp:egddpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_pre\_topc~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}((X0=k2\_topgen\_3){\unicdbdjded}((u1\_struct\_0~X0=\\
k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
k1\_numbers))){\unicdcdcdhd}((u1\_pre\_topc~X0=k1\_cantor\_1~k1\_numbers~X1){\unicdcdcdhd}\\
(X1=ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k1\_numbers))~\\
({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k1\_numbers))~(\\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  (\preoh r1\_xxreal\_0~X3~X2){\unicdcdcdhd}(v1\_rat\_1~X3))~(\\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k3\_rcomp\_1~X2~X3))))))\end{array}
\label{hyp:egcdpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k1\_limfunc1~X0=k3\_xxreal\_1~k2\_xxreal\_0~\\
X0)\end{array}
\label{hyp:egbdpfmgjgngggfhogdgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdfdpfehpgahhgfgogpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v4\_pre\_topc~(k1\_limfunc1~X0)~k2\_topgen\_3){\unicdcdcdhd}\\
(m1\_subset\_1~(k1\_limfunc1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~k2\_topgen\_3))))\end{array}$$
\end{theorem}
\end{document}
