\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\_borsuk\_6 (TMbr5WdQZsqknMtBetk4dpRQnJrdWPyeLe4)}
\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 $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k4\_topmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_treal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_treal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_treal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k18\_borsuk\_1 : {\iota}$ be given.
Let $ k19\_borsuk\_1 : {\iota}$ be given.
Let $ k17\_borsuk\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k4\_topmetr~X0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k4\_topmetr~X0~\\
X1))){\unicdbdjdcd}(v5\_pre\_topc~(k3\_treal\_1~X0~X1~X2~X3)~(k4\_topmetr~k6\_numbers~\\
np\_\_1)~(k4\_topmetr~X0~X1))))))\end{array}
\label{hyp:ehidpfehchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k18\_borsuk\_1=k1\_treal\_1~k6\_numbers~np\_\_1){\unicdcdcdhd}(k19\_borsuk\_1=\\
k2\_treal\_1~k6\_numbers~np\_\_1)\end{array}
\label{hyp:ehfdpfehchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k4\_topmetr}~{k6\_numbers}}~{np\_\_1}}={k17\_borsuk\_1}}\label{hyp:ehcdadpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(m2\_subset\_1~np\_\_0~k1\_numbers~k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~np\_\_0~\\
k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_0~k1\_numbers))\end{array}
\label{hyp:dhahdgadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_0}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchadpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_topmetr}={k17\_borsuk\_1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfehpgahngfgehch}
\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 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_pre\_topc~X2){\unicdcdcdhd}(l1\_pre\_topc~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v5\_pre\_topc~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X1)~\\
(u1\_struct\_0~X2)){\unicdcdcdhd}((v5\_pre\_topc~X4~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k1\_partfun1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~\\
(u1\_struct\_0~X2)~X3~X4)){\unicdcdcdhd}((v1\_funct\_2~(k1\_partfun1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)~X3~X4)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}((v5\_pre\_topc~(k1\_partfun1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)~X3~X4)~X0~\\
X2){\unicdcdcdhd}(m1\_subset\_1~(k1\_partfun1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)~X3~X4)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X2)))))))))))\end{array}
\label{hyp:mgbdpfehpgahchfgbgmgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k17\_borsuk\_1){\unicdcdcdhd}((v1\_pre\_topc~k17\_borsuk\_1){\unicdcdcdhd}(\\
v2\_pre\_topc~k17\_borsuk\_1))\end{array}
\label{hyp:ggdgjdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_pre\_topc~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_borsuk\_2~X3~X0~X1~X2){\unicdbdjdcd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpfngbdpfcgpgchdhfhlgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}\\
((v1\_xreal\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~(u1\_struct\_0~(k4\_topmetr~X0~\\
X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~(k4\_topmetr~X0~X1)))))){\unicdbdjdcd}(\\
(v1\_funct\_1~(k3\_treal\_1~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k3\_treal\_1~\\
X0~X1~X2~X3)~(u1\_struct\_0~(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~\\
(k4\_topmetr~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~(k3\_treal\_1~X0~X1~X2~X3)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~\\
(k4\_topmetr~X0~X1)))))))\end{array}
\label{hyp:egehpflgddpfehchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k19\_borsuk\_1}}~{({{u1\_struct\_0}~{k17\_borsuk\_1}})}}\label{hyp:egehpflgbdjdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k18\_borsuk\_1}}~{({{u1\_struct\_0}~{k17\_borsuk\_1}})}}\label{hyp:egehpflgbdidpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{l1\_pre\_topc}~{k17\_borsuk\_1}}\label{hyp:egehpflgbdhdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k19\_borsuk\_1}={np\_\_1}}\label{hyp:egbdfdpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k18\_borsuk\_1}={k6\_numbers}}\label{hyp:egbdedpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfcgpgchdhfhlgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_borsuk\_2~X3~\\
X0~X1~X2){\unicdbdjdcd}((v5\_pre\_topc~X3~k5\_topmetr~X0){\unicdbdjdcd}((v1\_funct\_1~(k1\_partfun1~\\
(u1\_struct\_0~(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~(k4\_topmetr~\\
k6\_numbers~np\_\_1))~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)~\\
(k3\_treal\_1~k6\_numbers~np\_\_1~(k2\_treal\_1~k6\_numbers~np\_\_1)~(k1\_treal\_1~\\
k6\_numbers~np\_\_1))~X3)){\unicdcdcdhd}((v1\_funct\_2~(k1\_partfun1~(u1\_struct\_0~\\
(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~(k4\_topmetr~k6\_numbers~\\
np\_\_1))~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)~(k3\_treal\_1~\\
k6\_numbers~np\_\_1~(k2\_treal\_1~k6\_numbers~np\_\_1)~(k1\_treal\_1~k6\_numbers~\\
np\_\_1))~X3)~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v5\_pre\_topc~\\
(k1\_partfun1~(u1\_struct\_0~(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~\\
(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
X0)~(k3\_treal\_1~k6\_numbers~np\_\_1~(k2\_treal\_1~k6\_numbers~np\_\_1)~\\
(k1\_treal\_1~k6\_numbers~np\_\_1))~X3)~k5\_topmetr~X0){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_partfun1~(u1\_struct\_0~(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~\\
(k4\_topmetr~k6\_numbers~np\_\_1))~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
X0)~(k3\_treal\_1~k6\_numbers~np\_\_1~(k2\_treal\_1~k6\_numbers~np\_\_1)~\\
(k1\_treal\_1~k6\_numbers~np\_\_1))~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~X0)))))))))))\end{array}$$
\end{theorem}
\end{document}
