\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{t13\_jgraph\_6 (TMRX829p79fM6p2eyuXqTJ8brxTkWmJZJ2G)}
\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 $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\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 $ k3\_topmetr : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\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}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\\
v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X3~X0~k3\_topmetr){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k15\_euclid~X1))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))))))){\unicdbdjdcd}\\
(\preoh ({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))~X4~X5=k1\_rlvect\_1~\\
(k15\_euclid~X1)~X2~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)~\\
X3~X5))){\unicdcdcdhd}(v5\_pre\_topc~X4~X0~(k15\_euclid~X1))))))))\end{array}
\label{hyp:ehjdpfkghgchbgahigpfgd}
\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 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k15\_euclid~X1))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k15\_euclid~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~\\
X2~X0~(k15\_euclid~X1)){\unicdcdcdhd}((v5\_pre\_topc~X3~X0~(k15\_euclid~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k15\_euclid~X1))){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))))))){\unicdbdjdcd}(\preoh ({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k15\_euclid~X1))~X4~X5=k3\_rlvect\_1~(k15\_euclid~X1)~\\
(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))~X2~\\
X5)~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))~\\
X3~X5))){\unicdcdcdhd}(v5\_pre\_topc~X4~X0~(k15\_euclid~X1)))))))))\end{array}
\label{hyp:ehbdcdpfkghgchbgahigpfgd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfkghgchbgahigpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~(k15\_euclid~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}\\
((v1\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(\\
m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k3\_topmetr)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~\\
X5~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~X5~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}\\
(\preoh (v5\_pre\_topc~X4~X0~k3\_topmetr){\unicdcdcdhd}((v5\_pre\_topc~X5~X0~k3\_topmetr){\unicdcdcdhd}\\
({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~(k15\_euclid~X1))){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))))))){\unicdbdjdcd}\\
(\preoh ({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k15\_euclid~X1))~X6~X7=k3\_rlvect\_1~\\
(k15\_euclid~X1)~(k1\_rlvect\_1~(k15\_euclid~X1)~X2~(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)~X4~X7))~(k1\_rlvect\_1~(k15\_euclid~\\
X1)~X3~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)~X5~\\
X7)))){\unicdcdcdhd}(v5\_pre\_topc~X6~X0~(k15\_euclid~X1)))))))))))\end{array}$$
\end{theorem}
\end{document}
