\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{t24\_borsuk\_1 (TMbdTyjRKudvGJmChUZUnrL1pA7p1jnxupc)}
\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ k2\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}((k8\_mcart\_1~\\
X0~X1~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((k1\_funct\_1~(k1\_funct\_3~(k9\_funct\_3~\\
X0~X1))~(k8\_mcart\_1~X0~X1~X2~X3)=X2){\unicdcdcdhd}(k1\_funct\_1~(k1\_funct\_3~(k10\_funct\_3~\\
X0~X1))~(k8\_mcart\_1~X0~X1~X2~X3)=X3))))\end{array}
\label{hyp:ehfdadpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\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~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}(k8\_mcart\_1~\\
X0~X1~X2~X3=k2\_zfmisc\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfngdgbgchehpfbd}
\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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0)){\unicdcdcdhd}(((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1)){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1)))))){\unicdbdjdcd}(k3\_borsuk\_1~X0~X1~X2~X3=k2\_zfmisc\_1~X2~\\
X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\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)))))){\unicdbdjdcd}(k2\_funct\_3~X0~X1~X2=k1\_funct\_3~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggfhogdgehpfdd}
\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}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_pre\_topc~X1~X0)))\end{array}
\label{hyp:chdghdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_funct\_1~(k9\_funct\_3~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k9\_funct\_3~X0~X1)~(k2\_zfmisc\_1~X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k9\_funct\_3~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X0))))\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpfdd}
\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}((v1\_funct\_1~(k9\_borsuk\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k9\_borsuk\_1~\\
X0~X1)~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~\\
(u1\_struct\_0~X1))){\unicdcdcdhd}(m1\_subset\_1~(k9\_borsuk\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~\\
(k9\_setfam\_1~(u1\_struct\_0~X1)))))))\end{array}
\label{hyp:egehpflgjdpfcgpgchdhfhlgpfbd}
\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}((v1\_funct\_1~(k8\_borsuk\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_borsuk\_1~\\
X0~X1)~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~(k8\_borsuk\_1~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~\\
(k9\_setfam\_1~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpflgidpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0)){\unicdcdcdhd}(((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1)){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1)))))){\unicdbdjdcd}(m1\_subset\_1~(k3\_borsuk\_1~X0~X1~X2~X3)~(\\
k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1))))\end{array}
\label{hyp:egehpflgddpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_funct\_1~(k10\_funct\_3~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k10\_funct\_3~X0~X1)~(k2\_zfmisc\_1~X0~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k10\_funct\_3~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X1))))\end{array}
\label{hyp:egehpflgbdadpfggfhogdgehpfdd}
\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}(k9\_borsuk\_1~X0~X1=k2\_funct\_3~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~X1)~(k10\_funct\_3~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1))))\end{array}
\label{hyp:egfdpfcgpgchdhfhlgpfbd}
\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}(k8\_borsuk\_1~X0~X1=k2\_funct\_3~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~X0)~(k9\_funct\_3~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1))))\end{array}
\label{hyp:egedpfcgpgchdhfhlgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfcgpgchdhfhlgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}((k3\_borsuk\_1~X0~X1~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((k3\_funct\_2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~(u1\_struct\_0~\\
X0))~(k8\_borsuk\_1~X0~X1)~(k3\_borsuk\_1~X0~X1~X2~X3)=X2){\unicdcdcdhd}(k3\_funct\_2~\\
(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X0~X1)))~(k9\_setfam\_1~\\
(u1\_struct\_0~X1))~(k9\_borsuk\_1~X0~X1)~(k3\_borsuk\_1~X0~X1~X2~X3)=\\
X3))))))\end{array}$$
\end{theorem}
\end{document}
