\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{t39\_topgen\_5 (TML1xVjDFH82mbJrppp5vYHe7YQGJgD63JZ)}
\maketitle
Let $ v2\_topgen\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_topgen\_5 : {\iota}$ be given.
Let $ k1\_topgen\_5 : {\iota}$ be given.
Let $ k3\_topgen\_5 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_topgen\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_topgen\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_topgen\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{({{{k4\_xboole\_0}~{X0}}~{X1}})}}~{X0}}}}\label{hyp:ehddgdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~k3\_topgen\_5))){\unicdbdjdcd}\\
((X0=k7\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~k2\_topgen\_5~\\
k1\_topgen\_5){\unicdbdjdcd}({\unicdcdadad} X1 .  k2\_pre\_topc~k3\_topgen\_5~(k7\_subset\_1~\\
(u1\_struct\_0~k3\_topgen\_5)~X0~(k1\_tarski~X1))=k2\_struct\_0~k3\_topgen\_5))\end{array}
\label{hyp:ehddddpfehpgahhgfgogpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\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}(\preoh v2\_struct\_0~k3\_topgen\_5){\unicdcdcdhd}((v1\_pre\_topc~k3\_topgen\_5){\unicdcdcdhd}((v2\_pre\_topc~\\
k3\_topgen\_5){\unicdcdcdhd}(l1\_pre\_topc~k3\_topgen\_5)))\end{array}
\label{hyp:egehpflgddpfehpgahhgfgogpffd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_topgen\_5}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{({{k15\_euclid}~{np\_\_2}})}})}})}}\label{hyp:egehpflgcdpfehpgahhgfgogpffd}
\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~(u1\_struct\_0~X0))){\unicdbdjdcd}((v2\_topgen\_1~\\
X1~X0){\unicdbdjded}(r1\_tarski~X1~(k2\_topgen\_1~X0~X1))))\end{array}
\label{hyp:eghdpfehpgahhgfgogpfbd}
\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=k3\_topgen\_5){\unicdbdjded}((u1\_struct\_0~X0=\\
k2\_topgen\_5){\unicdcdcdhd}({\unicdcdaddd} X1 .  (m1\_topgen\_2~X1~X0){\unicdcdcdhd}(({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(k1\_funct\_1~X1~(k19\_euclid~X2~k6\_numbers)=\\
ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k1\_numbers))~({\uniddcgcg} X3 : \\
\iota .  \preoh r1\_xxreal\_0~X3~k6\_numbers)~({\uniddcgcg} X3 : \iota .  k4\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_topreal9~np\_\_2~(k19\_euclid~X2~X3)~X3)~(\\
k6\_domain\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k19\_euclid~X2~k6\_numbers))))){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X3~k6\_numbers){\unicdbdjdcd}(k1\_funct\_1~X1~\\
(k19\_euclid~X2~X3)=ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~\\
k1\_numbers))~({\uniddcgcg} X4 : \iota .  \preoh r1\_xxreal\_0~X4~k6\_numbers)~({\uniddcgcg} X4 : \\
\iota .  k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_topreal9~\\
np\_\_2~(k19\_euclid~X2~X3)~X4)~k2\_topgen\_5)))))))))\end{array}
\label{hyp:egddpfehpgahhgfgogpffd}
\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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((X2=k2\_topgen\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in \\
u1\_struct\_0~X0){\unicdbdjdcd}((X3 \in X2){\unicdbdjded}(r1\_topgen\_1~X0~X1~X3))))))\end{array}
\label{hyp:egddpfehpgahhgfgogpfbd}
\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\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (r1\_topgen\_1~X0~X1~X2){\unicdbdjded}(X2 \in k2\_pre\_topc~\\
X0~(k7\_subset\_1~(u1\_struct\_0~X0)~X1~(k1\_tarski~X2)))))\end{array}
\label{hyp:egcdpfehpgahhgfgogpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfehpgahhgfgogpffd}
$$\begin{array}{c}(v2\_topgen\_1~(k7\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~k2\_topgen\_5~\\
k1\_topgen\_5)~k3\_topgen\_5){\unicdcdcdhd}(m1\_subset\_1~(k7\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~k2\_topgen\_5~k1\_topgen\_5)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
k3\_topgen\_5)))\end{array}$$
\end{theorem}
\end{document}
