\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{l27\_jgraph\_4 (TMKvQ6DgjjAABHAuqLtaK3J9xiBJfpqzjo9)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\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 $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_jgraph\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ l1\_pre\_topc : {{\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 $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(u1\_struct\_0~(k1\_pre\_topc~X0~X1)=X1))\end{array}
\label{hyp:ehidpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}((k12\_euclid~\\
X1=k6\_numbers){\unicdbdjdcd}(X1=k4\_struct\_0~(k15\_euclid~X0))))\end{array}
\label{hyp:ehcdedpfehpgahchogdhpfbd}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(((v1\_funct\_1~(k2\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~k3\_topmetr)~(k1\_jgraph\_4~\\
np\_\_2)~X0)){\unicdcdcdhd}((v1\_funct\_2~(k2\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~(u1\_struct\_0~k3\_topmetr)~(k1\_jgraph\_4~np\_\_2)~X0)~(u1\_struct\_0~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}\\
((v5\_pre\_topc~(k2\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(u1\_struct\_0~k3\_topmetr)~(k1\_jgraph\_4~np\_\_2)~X0)~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X0)~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~(k2\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(u1\_struct\_0~k3\_topmetr)~(k1\_jgraph\_4~\\
np\_\_2)~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X0))~(u1\_struct\_0~k3\_topmetr))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~\\
X0))){\unicdbdjdcd}(k1\_funct\_1~(k2\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(u1\_struct\_0~k3\_topmetr)~(k1\_jgraph\_4~np\_\_2)~X0)~X1=k1\_funct\_1~\\
(k1\_jgraph\_4~np\_\_2)~X1)))\end{array}
\label{hyp:mgcdgdpfkghgchbgahigpfed}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_funct\_1~(k1\_jgraph\_4~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k1\_jgraph\_4~X0)~(u1\_struct\_0~(k15\_euclid~X0))~(\\
u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~(k1\_jgraph\_4~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0))~(u1\_struct\_0~k3\_topmetr))))))\end{array}
\label{hyp:egehpflgbdpfkghgchbgahigpfed}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~(u1\_struct\_0~(k15\_euclid~X0))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
X0))~(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}((X1=k1\_jgraph\_4~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(k3\_funct\_2~(\\
u1\_struct\_0~(k15\_euclid~X0))~(u1\_struct\_0~k3\_topmetr)~X1~X2=k12\_euclid~\\
X2))))\end{array}
\label{hyp:egbdpfkghgchbgahigpfed}
\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:mgcdhdpfkghgchbgahigpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~\\
X0))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))~\\
(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}(((X1=k2\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(u1\_struct\_0~k3\_topmetr)~(k1\_jgraph\_4~np\_\_2)~\\
X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(\preoh (X2 \in u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0)){\unicdcdcdhd}(X2=\\
k4\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))){\unicdbdjdcd}(k3\_funct\_2~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))~(u1\_struct\_0~\\
k3\_topmetr)~X1~X2{\unicdcdgdad}k6\_numbers))))\end{array}$$
\end{theorem}
\end{document}
