\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{t28\_topalg\_4 (TMG1HyWYuZufJtiao1DAkkZxfFkQwnLeuR9)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_topalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_topalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k10\_topalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_topalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\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 .  \\
(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 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k5\_topalg\_1~(k2\_borsuk\_1~X0~X1)~(k4\_borsuk\_1~X0~\\
X1~X2~X3)))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_borsuk\_2~X5~(k2\_borsuk\_1~X0~X1)~(k4\_borsuk\_1~\\
X0~X1~X2~X3)~(k4\_borsuk\_1~X0~X1~X2~X3)){\unicdbdjdcd}((X4=k6\_eqrel\_1~(k2\_topalg\_1~\\
(k2\_borsuk\_1~X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3))~(k2\_topalg\_1~(k2\_borsuk\_1~\\
X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3))~(k4\_topalg\_1~(k2\_borsuk\_1~X0~X1)~\\
(k4\_borsuk\_1~X0~X1~X2~X3))~X5){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~(k5\_topalg\_1~\\
(k2\_borsuk\_1~X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3)))~(u1\_struct\_0~(k2\_group\_7~\\
(k2\_tarski~np\_\_1~np\_\_2)~(k10\_finseq\_1~(k5\_topalg\_1~X0~X2)~(k5\_topalg\_1~\\
X1~X3))))~(k11\_topalg\_4~X0~X1~X2~X3)~X4=k10\_finseq\_1~(k6\_eqrel\_1~\\
(k2\_topalg\_1~X0~X2)~(k2\_topalg\_1~X0~X2)~(k4\_topalg\_1~X0~X2)~(k9\_topalg\_4~\\
X0~X1~X2~X3~X5))~(k6\_eqrel\_1~(k2\_topalg\_1~X1~X3)~(k2\_topalg\_1~X1~X3)~\\
(k4\_topalg\_1~X1~X3)~(k10\_topalg\_4~X0~X1~X2~X3~X5)))))))))\end{array}
\label{hyp:ehcdhdpfehpgahbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\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}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_borsuk\_1~X0~X1)){\unicdcdcdhd}((v1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1)){\unicdcdcdhd}(v2\_pre\_topc~(k2\_borsuk\_1~X0~X1))))\end{array}
\label{hyp:ggdgfdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~X1))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_borsuk\_1~\\
X0~X1~X2~X3)~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))\end{array}
\label{hyp:egehpflgedpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}((v1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1)){\unicdcdcdhd}((v2\_pre\_topc~(k2\_borsuk\_1~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(k2\_borsuk\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgcdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~X1))))){\unicdbdjdcd}((v1\_funct\_1~(k11\_topalg\_4~\\
X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k11\_topalg\_4~X0~X1~X2~X3)~(u1\_struct\_0~\\
(k5\_topalg\_1~(k2\_borsuk\_1~X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3)))~(u1\_struct\_0~\\
(k2\_group\_7~(k2\_tarski~np\_\_1~np\_\_2)~(k10\_finseq\_1~(k5\_topalg\_1~\\
X0~X2)~(k5\_topalg\_1~X1~X3))))){\unicdcdcdhd}(m1\_subset\_1~(k11\_topalg\_4~X0~X1~\\
X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k5\_topalg\_1~(k2\_borsuk\_1~\\
X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3)))~(u1\_struct\_0~(k2\_group\_7~(k2\_tarski~\\
np\_\_1~np\_\_2)~(k10\_finseq\_1~(k5\_topalg\_1~X0~X2)~(k5\_topalg\_1~X1~\\
X3)))))))))\end{array}
\label{hyp:egehpflgbdbdpfehpgahbgmghgpfed}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfehpgahbgmghgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_borsuk\_2~X4~\\
(k2\_borsuk\_1~X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3)~(k4\_borsuk\_1~X0~X1~X2~\\
X3)){\unicdbdjdcd}(k1\_funct\_1~(k11\_topalg\_4~X0~X1~X2~X3)~(k6\_eqrel\_1~(k2\_topalg\_1~\\
(k2\_borsuk\_1~X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3))~(k2\_topalg\_1~(k2\_borsuk\_1~\\
X0~X1)~(k4\_borsuk\_1~X0~X1~X2~X3))~(k4\_topalg\_1~(k2\_borsuk\_1~X0~X1)~\\
(k4\_borsuk\_1~X0~X1~X2~X3))~X4)=k10\_finseq\_1~(k6\_eqrel\_1~(k2\_topalg\_1~\\
X0~X2)~(k2\_topalg\_1~X0~X2)~(k4\_topalg\_1~X0~X2)~(k9\_topalg\_4~X0~X1~\\
X2~X3~X4))~(k6\_eqrel\_1~(k2\_topalg\_1~X1~X3)~(k2\_topalg\_1~X1~X3)~(k4\_topalg\_1~\\
X1~X3)~(k10\_topalg\_4~X0~X1~X2~X3~X4)))))))\end{array}$$
\end{theorem}
\end{document}
