\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{t33\_topgen\_3 (TMYJxoaMp2dSVdWzZ3ShLnLhwJRpncZf3hP)}
\maketitle
Let $ k2\_waybel23 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_topgen\_3 : {\iota}$ be given.
Let $ k3\_topgen\_3 : {\iota}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_cantor\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_tops\_2 : {{\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 $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_rat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_cantor\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ c1\_\_topgen\_3 : {\iota}$ be given.
Let $ v1\_finset\_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 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdaddd} X1 .  ((v1\_cantor\_1~X1~X0){\unicdcdcdhd}\\
((v1\_tops\_2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))){\unicdcdcdhd}(k1\_card\_1~X1=k2\_waybel23~X0))\end{array}
\label{hyp:ehhdedpfhhbgjhcgfgmgcddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_cantor\_1~X1~X0){\unicdcdcdhd}\\
((v1\_tops\_2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))){\unicdbdjdcd}(r1\_ordinal1~(k2\_waybel23~X0)~(k1\_card\_1~\\
X1)))\end{array}
\label{hyp:ehhdddpfhhbgjhcgfgmgcddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}((X0 \in X1){\unicdbdjded}\\
(\preoh r1\_ordinal1~X1~X0)))\end{array}
\label{hyp:ehedpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(\preoh (k1\_card\_1~X0 \in k3\_topgen\_3){\unicdcdcdhd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (v1\_rat\_1~X2){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}(\preoh k3\_rcomp\_1~\\
X1~X2 \in k1\_cantor\_1~k1\_numbers~X0)))))\end{array}
\label{hyp:ehddcdpfehpgahhgfgogpfdd}
\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\_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}k1\_card\_1~(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))=k3\_topgen\_3\end{array}
\label{hyp:ehcdadpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((v3\_pre\_topc~\\
(k3\_rcomp\_1~X0~X1)~k2\_topgen\_3){\unicdcdcdhd}(m1\_subset\_1~(k3\_rcomp\_1~X0~X1)~\\
(k1\_zfmisc\_1~(u1\_struct\_0~k2\_topgen\_3)))))\end{array}
\label{hyp:ehbdbdpfehpgahhgfgogpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_ordinal1~X0~X1){\unicdbdjded}(r1\_tarski~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:mgcdadpfehpgahhgfgogpfdd}
\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}
{{({\preoh{{{v1\_finset\_1}~{k3\_topgen\_3}}}})}{\unicdcdcdhd}{({{v1\_card\_1}~{k3\_topgen\_3}})}}\label{hyp:egehpflgddpfehpgahhgfgogpfdd}
\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}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\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 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((v3\_pre\_topc~X1~X0){\unicdbdjded}(X1 \in u1\_pre\_topc~X0)))\end{array}
\label{hyp:egcdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_rat\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddddpfehpgahhgfgogpfdd}
${{{k2\_waybel23}~{k2\_topgen\_3}}={k3\_topgen\_3}}$.
\end{theorem}
\end{document}
