\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{t41\_jordan (TMQPSzBPxgySPxzgXdgZryaYt6AiVpwtyT7)}
\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 $ k6\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_funct\_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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_borsuk\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_struct\_0 : {{\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 .  \\
((v3\_funct\_1~X2){\unicdcdcdhd}(m1\_borsuk\_2~X2~X0~X1~X1)){\unicdbdjdcd}(r2\_funct\_2~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~X0)~X2~(k6\_struct\_0~k5\_topmetr~X0~X1))))\end{array}
\label{hyp:ehfdpfcgpgchdhfhlgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((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}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\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 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}\\
(l1\_pre\_topc~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
(m1\_borsuk\_2~X2~X0~X1~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}\\
((v4\_relat\_1~X2~(u1\_struct\_0~k5\_topmetr)){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v3\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~(u1\_struct\_0~\\
k5\_topmetr)){\unicdcdcdhd}(v1\_funct\_2~X2~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
X0))))))))))\end{array}
\label{hyp:chdgedpfcgpgchdhfhlgpfcd}
\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 .  (((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_pre\_topc~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(u1\_struct\_0~X1)))){\unicdbdjdcd}((v1\_funct\_1~(k6\_struct\_0~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~\\
(k6\_struct\_0~X0~X1~X2)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(v5\_pre\_topc~\\
(k6\_struct\_0~X0~X1~X2)~X0~X1)))\end{array}
\label{hyp:ggdgfdpfahchfgpfehpgahdg}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X1)))){\unicdbdjdcd}(\\
(v1\_funct\_1~(k6\_struct\_0~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k6\_struct\_0~\\
X0~X1~X2)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k6\_struct\_0~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))))))\end{array}
\label{hyp:egehpflggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{l1\_pre\_topc}~{k17\_borsuk\_1}}\label{hyp:egehpflgbdhdpfcgpgchdhfhlgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfkgpgchegbgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(m1\_borsuk\_2~\\
(k6\_struct\_0~k5\_topmetr~X0~X1)~X0~X1~X1))\end{array}$$
\end{theorem}
\end{document}
