\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{t25\_waybel29 (TMXxT9qFSp7uVQyHXandtd4EhiR9DXQRaZ4)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v23\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_waybel29 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_borsuk\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_waybel24 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_waybel29 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_waybel11 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_yellow\_9 : {{\iota}{\unicdbdjdcd}{{\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 $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_connsp\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\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 $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_waybel26 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}((v3\_waybel\_3~(k2\_yellow\_1~(u1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_waybel11~X1){\unicdcdcdhd}(m1\_yellow\_9~X1~(k2\_yellow\_1~\\
(u1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_pre\_topc~X3~X0){\unicdcdcdhd}(m1\_connsp\_2~X3~X0~X2)){\unicdbdjdcd}\\
({\unicdcdaddd} X4 .  ((v3\_pre\_topc~X4~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1)))){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(m1\_connsp\_2~(k1\_setfam\_1~X4)~\\
X0~X2)))))))\end{array}
\label{hyp:mgddgdpfhhbgjhcgfgmgcdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}(({\unicdcdadad} X1 .  ((v4\_waybel11~X1){\unicdcdcdhd}(m1\_yellow\_9~\\
X1~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_pre\_topc~X3~X0){\unicdcdcdhd}(m1\_connsp\_2~\\
X3~X0~X2)){\unicdbdjdcd}({\unicdcdaddd} X4 .  ((v3\_pre\_topc~X4~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1)))){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(m1\_connsp\_2~(k1\_setfam\_1~X4)~\\
X0~X2)))))){\unicdbdjdcd}(v3\_waybel\_3~(k2\_yellow\_1~(u1\_pre\_topc~X0))))\end{array}
\label{hyp:mgddfdpfhhbgjhcgfgmgcdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}(({\unicdcdadad} X1 .  ((v4\_waybel11~X1){\unicdcdcdhd}(m1\_yellow\_9~\\
X1~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_pre\_topc~X3~X0){\unicdcdcdhd}(m1\_connsp\_2~\\
X3~X0~X2)){\unicdbdjdcd}({\unicdcdaddd} X4 .  ((v3\_pre\_topc~X4~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1)))){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(m1\_connsp\_2~(k1\_setfam\_1~X4)~\\
X0~X2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}\\
(l1\_pre\_topc~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_waybel11~X2){\unicdcdcdhd}(m1\_yellow\_9~\\
X2~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)){\unicdcdcdhd}((v5\_pre\_topc~\\
X3~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X2))))))){\unicdbdjdcd}((v3\_pre\_topc~(k5\_waybel26~X3)~(k2\_borsuk\_1~\\
X1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k5\_waybel26~X3)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k2\_borsuk\_1~X1~X0)))))))))\end{array}
\label{hyp:mgddedpfhhbgjhcgfgmgcdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}(({\unicdcdadad} X1 .  ((v4\_waybel11~X1){\unicdcdcdhd}(m1\_yellow\_9~\\
X1~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}((v3\_pre\_topc~(ReplSep2~\\
(toset~({\uniddcgcg} X2 : \iota .  (v3\_pre\_topc~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))))~({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  X3 \in X2)~({\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  k4\_tarski~X2~X3))~(k2\_borsuk\_1~X1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  (v3\_pre\_topc~X2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))~({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  \\
X3 \in X2)~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k4\_tarski~X2~X3))~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~X1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_waybel11~\\
X1){\unicdcdcdhd}(m1\_yellow\_9~X1~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_pre\_topc~\\
X3~X0){\unicdcdcdhd}(m1\_connsp\_2~X3~X0~X2)){\unicdbdjdcd}({\unicdcdaddd} X4 .  ((v3\_pre\_topc~X4~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X1)))){\unicdcdcdhd}((X3 \in X4){\unicdcdcdhd}(\\
m1\_connsp\_2~(k1\_setfam\_1~X4)~X0~X2)))))))\end{array}
\label{hyp:mgddddpfhhbgjhcgfgmgcdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_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 .  ((v4\_waybel11~\\
X2){\unicdcdcdhd}(m1\_yellow\_9~X2~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2)){\unicdcdcdhd}((v5\_pre\_topc~X3~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))))))){\unicdbdjdcd}((v3\_pre\_topc~(k5\_waybel26~\\
X3)~(k2\_borsuk\_1~X1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k5\_waybel26~X3)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~X1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_waybel11~\\
X1){\unicdcdcdhd}(m1\_yellow\_9~X1~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}((v3\_pre\_topc~\\
(ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  (v3\_pre\_topc~X2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))~({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  \\
X3 \in X2)~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k4\_tarski~X2~X3))~(k2\_borsuk\_1~\\
X1~X0)){\unicdcdcdhd}(m1\_subset\_1~(ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  (v3\_pre\_topc~\\
X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))~({\uniddcgcg} X2 : \\
\iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  X3 \in X2)~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k4\_tarski~X2~\\
X3))~(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0)))))))\end{array}
\label{hyp:mgddcdpfhhbgjhcgfgmgcdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_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 .  ((v4\_waybel11~\\
X2){\unicdcdcdhd}(m1\_yellow\_9~X2~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2)){\unicdcdcdhd}((v5\_pre\_topc~X3~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))))))){\unicdbdjdcd}((v3\_pre\_topc~(k5\_waybel26~\\
X3)~(k2\_borsuk\_1~X1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k5\_waybel26~X3)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_borsuk\_1~X1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}(v23\_waybel\_0~(k3\_waybel29~\\
X1~X0)~(k2\_yellow\_1~(u1\_pre\_topc~(k2\_borsuk\_1~X1~X0)))~(k3\_waybel24~\\
X1~(k1\_waybel29~(k2\_yellow\_1~(u1\_pre\_topc~X0)))))))\end{array}
\label{hyp:mgddbdpfhhbgjhcgfgmgcdjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_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}(v23\_waybel\_0~(k3\_waybel29~\\
X1~X0)~(k2\_yellow\_1~(u1\_pre\_topc~(k2\_borsuk\_1~X1~X0)))~(k3\_waybel24~\\
X1~(k1\_waybel29~(k2\_yellow\_1~(u1\_pre\_topc~X0)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v4\_waybel11~X2){\unicdcdcdhd}(m1\_yellow\_9~X2~(k2\_yellow\_1~(u1\_pre\_topc~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X2)){\unicdcdcdhd}((v5\_pre\_topc~X3~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))))))){\unicdbdjdcd}\\
((v3\_pre\_topc~(k5\_waybel26~X3)~(k2\_borsuk\_1~X1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k5\_waybel26~X3)~(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_borsuk\_1~X1~X0)))))))))\end{array}
\label{hyp:mgcdjdpfhhbgjhcgfgmgcdjd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfhhbgjhcgfgmgcdjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v6\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}((v3\_waybel\_3~(k2\_yellow\_1~(u1\_pre\_topc~\\
X0))){\unicdbdjded}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}(v23\_waybel\_0~(k3\_waybel29~X1~X0)~(k2\_yellow\_1~(u1\_pre\_topc~\\
(k2\_borsuk\_1~X1~X0)))~(k3\_waybel24~X1~(k1\_waybel29~(k2\_yellow\_1~\\
(u1\_pre\_topc~X0)))))))\end{array}$$
\end{theorem}
\end{document}
