\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{t19\_borsuk\_6 (TMNei3nSbQEXJ22TajCS3nH9JPtTgxkhsHT)}
\maketitle
Let $ v4\_pre\_topc : {{\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 $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(v4\_pre\_topc~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k9\_real\_1~np\_\_1~\\
(k8\_real\_1~np\_\_2~(k17\_euclid~X0)))~(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  \\
X0))~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X0 : \\
\iota .  m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \\
\iota .  r1\_xxreal\_0~(k9\_real\_1~np\_\_1~(k8\_real\_1~np\_\_2~(k17\_euclid~\\
X0)))~(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:ehbdidpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v4\_pre\_topc~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k9\_real\_1~(k8\_real\_1~\\
np\_\_2~(k17\_euclid~X0))~np\_\_1)~(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  X0))~\\
(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  \\
m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  \\
r1\_xxreal\_0~(k9\_real\_1~(k8\_real\_1~np\_\_2~(k17\_euclid~X0))~np\_\_1)~\\
(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:ehbdgdpfcgpgchdhfhlgpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X2 .  ReplSep~\\
(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~X2))~({\uniddcgcg} X3 : \iota .  (X1~X3){\unicdcdcdhd}(\\
X0~X3))~({\uniddcgcg} X3 : \iota .  X3)=k3\_xboole\_0~(ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~X2))~({\uniddcgcg} X3 : \iota .  X1~X3)~({\uniddcgcg} X3 : \iota .  X3))~(\\
ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~X2))~({\uniddcgcg} X3 : \iota .  X0~\\
X3)~({\uniddcgcg} X3 : \iota .  X3))\end{array}
\label{hyp:dhbdadpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v2\_pre\_topc~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v13\_algstr\_0~(k15\_euclid~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v3\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v5\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v7\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}((v8\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
(v5\_rltopsp1~(k15\_euclid~X0)))))))))))\end{array}
\label{hyp:ggdggdpffgfhdgmgjgeg}
\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}(((v4\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((v4\_pre\_topc~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}(v4\_pre\_topc~(k3\_xboole\_0~X1~X2)~X0)\end{array}
\label{hyp:ggdgedpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_rltopsp1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{X0}})}})}}}\label{hyp:egehpfmgbdpfchmgehpgahdhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(m1\_subset\_1~(k9\_subset\_1~X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v5\_rltopsp1~(k15\_euclid~X0)){\unicdcdcdhd}\\
(l1\_rltopsp1~(k15\_euclid~X0)))\end{array}
\label{hyp:egehpflgbdfdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfcgpgchdhfhlgpfgd}
$$\begin{array}{c}(v4\_pre\_topc~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  (r1\_xxreal\_0~(k9\_real\_1~np\_\_1~\\
(k8\_real\_1~np\_\_2~(k17\_euclid~X0)))~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k9\_real\_1~(k8\_real\_1~np\_\_2~(k17\_euclid~X0))~np\_\_1)~(k18\_euclid~\\
X0)))~({\uniddcgcg} X0 : \iota .  X0))~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~(ReplSep~\\
(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~\\
({\uniddcgcg} X0 : \iota .  (r1\_xxreal\_0~(k9\_real\_1~np\_\_1~(k8\_real\_1~np\_\_2~(\\
k17\_euclid~X0)))~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k9\_real\_1~(k8\_real\_1~\\
np\_\_2~(k17\_euclid~X0))~np\_\_1)~(k18\_euclid~X0)))~({\uniddcgcg} X0 : \iota .  X0))~\\
(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))\end{array}$$
\end{theorem}
\end{document}
