\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{t13\_topalg\_2 (TMGAZSwmfjBueTKuUdohfwNNDBVnmrZdAiG)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_topalg\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_topalg\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_topalg\_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 $ r1\_borsuk\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r4\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(X2 \in u1\_struct\_0~(k5\_topalg\_1~X0~X1)){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_borsuk\_2~\\
X3~X0~X1~X1){\unicdcdcdhd}(X2=k6\_eqrel\_1~(k2\_topalg\_1~X0~X1)~(k2\_topalg\_1~X0~\\
X1)~(k4\_topalg\_1~X0~X1)~X3))))\end{array}
\label{hyp:ehedhdpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_borsuk\_6~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_borsuk\_2~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_borsuk\_2~X4~X0~X1~X2){\unicdbdjdcd}\\
((k6\_eqrel\_1~(k1\_topalg\_1~X0~X1~X2)~(k1\_topalg\_1~X0~X1~X2)~(k3\_topalg\_1~\\
X0~X1~X2)~X3=k6\_eqrel\_1~(k1\_topalg\_1~X0~X1~X2)~(k1\_topalg\_1~X0~X1~\\
X2)~(k3\_topalg\_1~X0~X1~X2)~X4){\unicdbdjded}(r3\_borsuk\_2~X0~X1~X2~X3~X4)))))))\end{array}
\label{hyp:ehedgdpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_topalg\_2~X0){\unicdcdcdhd}(m1\_pre\_topc~\\
X0~k2\_topalg\_2))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_borsuk\_2~\\
X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_borsuk\_2~X4~X0~X1~X2){\unicdbdjdcd}(r4\_borsuk\_2~\\
X0~X1~X2~X3~X4)))))\end{array}
\label{hyp:ehbdcdpfehpgahbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(r1\_borsuk\_6~X0~X1~X1)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v1\_borsuk\_2~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((m1\_borsuk\_2~X3~X0~X1~X2){\unicdcdcdhd}(m1\_borsuk\_2~X4~X0~X1~X2))))){\unicdbdjdcd}(\\
(r4\_borsuk\_2~X0~X1~X2~X3~X4){\unicdbdjded}(r3\_borsuk\_2~X0~X1~X2~X3~X4))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchedpfcgpgchdhfhlgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k6\_eqrel\_1~X0~X1~X2~X3=k9\_relat\_1~\\
X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_topalg\_2}={k3\_topmetr}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfehpgahbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
(m1\_borsuk\_2~X2~X0~X1~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}\\
((v4\_relat\_1~X2~(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}\\
((v1\_funct\_2~X2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
v5\_pre\_topc~X2~k5\_topmetr~X0)))))))))\end{array}
\label{hyp:chdgcdpfcgpgchdhfhlgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
(l1\_pre\_topc~X1))\end{array}
\label{hyp:egehpfngbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k4\_topalg\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_topalg\_1~X0~\\
X1)~(k2\_topalg\_1~X0~X1))))\end{array}
\label{hyp:egehpflgedpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v2\_pre\_topc}~{k3\_topmetr}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{k3\_topmetr}})}}\label{hyp:egehpflgddpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k4\_topalg\_1~\\
X0~X1=k3\_topalg\_1~X0~X1~X1))\end{array}
\label{hyp:egedpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k2\_topalg\_1~X0~X1=k1\_topalg\_1~\\
X0~X1~X1))\end{array}
\label{hyp:egcdpfehpgahbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_pre\_topc~X0~k2\_topalg\_2){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}\\
(v2\_topalg\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v1\_borsuk\_2~X0)))\end{array}
\label{hyp:dgdgddpfehpgahbgmghgpfcd}
\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\_pre\_topc~X1~X0){\unicdbdjdcd}(v2\_pre\_topc~X1))\end{array}
\label{hyp:dgdgbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfehpgahbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_topalg\_2~X0){\unicdcdcdhd}(m1\_pre\_topc~\\
X0~k2\_topalg\_2))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_borsuk\_2~X2~X0~X1~X1){\unicdbdjdcd}(u1\_struct\_0~(k5\_topalg\_1~\\
X0~X1)=k1\_tarski~(k6\_eqrel\_1~(k2\_topalg\_1~X0~X1)~(k2\_topalg\_1~\\
X0~X1)~(k4\_topalg\_1~X0~X1)~X2))))\end{array}$$
\end{theorem}
\end{document}
