\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{t46\_borsuk\_6 (TMQriF1caE4VqNNGgCzjkgJKvpRkpWJjb6D)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_borsuk\_2 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ v5\_pre\_topc : {{\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 $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r4\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k2\_borsuk\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ r1\_borsuk\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\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 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_borsuk\_2~X3~\\
X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~X4~k5\_topmetr~\\
k5\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~k5\_topmetr))))))){\unicdbdjdcd}(((k1\_funct\_1~X4~\\
k6\_numbers=k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~X4~np\_\_1=np\_\_1){\unicdcdcdhd}(r1\_borsuk\_6~\\
X0~X1~X2))){\unicdbdjdcd}(r3\_borsuk\_2~X0~X1~X2~(k2\_borsuk\_6~X0~X1~X2~X3~X4)~X3))))))\end{array}
\label{hyp:ehedfdpfcgpgchdhfhlgpfgd}
\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 .  (((\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~X2){\unicdbdjded}(r1\_borsuk\_2~\\
X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfcgpgchdhfhlgpfgd}
\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}(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}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~X4~k5\_topmetr~k5\_topmetr){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~k5\_topmetr))))))))))){\unicdbdjdcd}(m1\_borsuk\_2~(k2\_borsuk\_6~\\
X0~X1~X2~X3~X4)~X0~X1~X2)\end{array}
\label{hyp:egehpflgcdpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_borsuk\_2~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_borsuk\_2~X0~X1~X2))))\end{array}
\label{hyp:egddpfcgpgchdhfhlgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfcgpgchdhfhlgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v1\_borsuk\_2~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_borsuk\_2~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~\\
X4~k5\_topmetr~k5\_topmetr){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~k5\_topmetr))))))){\unicdbdjdcd}((\\
(k1\_funct\_1~X4~k6\_numbers=k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~X4~np\_\_1=\\
np\_\_1)){\unicdbdjdcd}(r4\_borsuk\_2~X0~X1~X2~(k2\_borsuk\_6~X0~X1~X2~X3~X4)~X3))))))\end{array}$$
\end{theorem}
\end{document}
