\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{l109\_borsuk\_7 (TMGBiDo1D7rkK6cZ6c7HQzBS64u6ifqE664)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_toprealb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ v2\_borsuk\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v3\_topalg\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ k8\_toprealb : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_borsuk\_7 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_borsuk\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ c18\_\_borsuk\_7 : {\iota}$ be given.
Let $ m1\_borsuk\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(u1\_struct\_0~(k7\_toprealb~\\
(k2\_nat\_1~np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~np\_\_2~\\
np\_\_1)))~np\_\_1))~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k7\_toprealb~(k2\_nat\_1~\\
np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~np\_\_2~np\_\_1)))~\\
np\_\_1))~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}(\preoh (\preoh v2\_borsuk\_7~\\
X0~(k2\_nat\_1~np\_\_2~np\_\_1)~np\_\_2~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~\\
np\_\_2~np\_\_1)))~np\_\_1){\unicdcdcdhd}((v5\_pre\_topc~X0~(k7\_toprealb~(k2\_nat\_1~\\
np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~np\_\_2~np\_\_1)))~\\
np\_\_1)~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((v3\_topalg\_6~(k1\_partfun1~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k8\_toprealb~np\_\_3))~(u1\_struct\_0~(\\
k8\_toprealb~(k1\_nat\_1~np\_\_2~np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~\\
np\_\_2))~(k14\_borsuk\_7~np\_\_1)~(k16\_borsuk\_7~np\_\_2~X0))~(k8\_toprealb~\\
np\_\_2)~(k3\_funct\_2~(u1\_struct\_0~(k8\_toprealb~(k2\_nat\_1~np\_\_2~\\
np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~np\_\_2))~(k16\_borsuk\_7~np\_\_2~\\
X0)~c18\_\_borsuk\_7)){\unicdcdcdhd}(m1\_borsuk\_2~(k1\_partfun1~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k8\_toprealb~np\_\_3))~(u1\_struct\_0~(\\
k8\_toprealb~(k1\_nat\_1~np\_\_2~np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~\\
np\_\_2))~(k14\_borsuk\_7~np\_\_1)~(k16\_borsuk\_7~np\_\_2~X0))~(k8\_toprealb~\\
np\_\_2)~(k3\_funct\_2~(u1\_struct\_0~(k8\_toprealb~(k2\_nat\_1~np\_\_2~\\
np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~np\_\_2))~(k16\_borsuk\_7~np\_\_2~\\
X0)~c18\_\_borsuk\_7)~(k3\_funct\_2~(u1\_struct\_0~(k8\_toprealb~(k2\_nat\_1~\\
np\_\_2~np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~np\_\_2))~(k16\_borsuk\_7~\\
np\_\_2~X0)~c18\_\_borsuk\_7)))))\end{array}
\label{hyp:mgbdadidpfcgpgchdhfhlgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(u1\_struct\_0~(k7\_toprealb~\\
(k2\_nat\_1~np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~np\_\_2~\\
np\_\_1)))~np\_\_1))~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k7\_toprealb~(k2\_nat\_1~\\
np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~np\_\_2~np\_\_1)))~\\
np\_\_1))~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}((v5\_pre\_topc~\\
X0~(k7\_toprealb~(k2\_nat\_1~np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~\\
(k2\_nat\_1~np\_\_2~np\_\_1)))~np\_\_1)~(k15\_euclid~np\_\_2)){\unicdbdjdcd}((v2\_borsuk\_7~\\
X0~(k2\_nat\_1~np\_\_2~np\_\_1)~np\_\_2~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~\\
np\_\_2~np\_\_1)))~np\_\_1){\unicdcdcdid}((v3\_topalg\_6~(k1\_partfun1~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k8\_toprealb~np\_\_3))~(u1\_struct\_0~(\\
k8\_toprealb~(k1\_nat\_1~np\_\_2~np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~\\
np\_\_2))~(k14\_borsuk\_7~np\_\_1)~(k16\_borsuk\_7~np\_\_2~X0))~(k8\_toprealb~\\
np\_\_2)~(k3\_funct\_2~(u1\_struct\_0~(k8\_toprealb~(k2\_nat\_1~np\_\_2~\\
np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~np\_\_2))~(k16\_borsuk\_7~np\_\_2~\\
X0)~c18\_\_borsuk\_7)){\unicdcdcdhd}(m1\_borsuk\_2~(k1\_partfun1~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k8\_toprealb~np\_\_3))~(u1\_struct\_0~(\\
k8\_toprealb~(k1\_nat\_1~np\_\_2~np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~\\
np\_\_2))~(k14\_borsuk\_7~np\_\_1)~(k16\_borsuk\_7~np\_\_2~X0))~(k8\_toprealb~\\
np\_\_2)~(k3\_funct\_2~(u1\_struct\_0~(k8\_toprealb~(k2\_nat\_1~np\_\_2~\\
np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~np\_\_2))~(k16\_borsuk\_7~np\_\_2~\\
X0)~c18\_\_borsuk\_7)~(k3\_funct\_2~(u1\_struct\_0~(k8\_toprealb~(k2\_nat\_1~\\
np\_\_2~np\_\_1)))~(u1\_struct\_0~(k8\_toprealb~np\_\_2))~(k16\_borsuk\_7~\\
np\_\_2~X0)~c18\_\_borsuk\_7)))))\end{array}
\label{hyp:mgbdadedpfcgpgchdhfhlgpfhd}
\end{equation}
\begin{theorem}\label{thm:mgbdadjdpfcgpgchdhfhlgpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(u1\_struct\_0~(k7\_toprealb~\\
(k2\_nat\_1~np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~np\_\_2~\\
np\_\_1)))~np\_\_1))~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v5\_pre\_topc~\\
X0~(k7\_toprealb~(k2\_nat\_1~np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~\\
(k2\_nat\_1~np\_\_2~np\_\_1)))~np\_\_1)~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k7\_toprealb~(k2\_nat\_1~\\
np\_\_2~np\_\_1)~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~np\_\_2~np\_\_1)))~\\
np\_\_1))~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))){\unicdbdjdcd}(v2\_borsuk\_7~\\
X0~(k2\_nat\_1~np\_\_2~np\_\_1)~np\_\_2~(k4\_struct\_0~(k15\_euclid~(k2\_nat\_1~\\
np\_\_2~np\_\_1)))~np\_\_1)\end{array}$$
\end{theorem}
\end{document}
