\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{t6\_jgraph\_4 (TMXGm62cdgCeGD3mc284qK3piEuB6xPFY5J)}
\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\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 $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}\\
(\preoh (v5\_pre\_topc~X1~X0~k3\_topmetr){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k3\_topmetr)))))){\unicdbdjdcd}(\preoh ({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}((k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)~X1~X3=X4){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)~X2~X3=k3\_xcmplx\_0~X4~X4)))){\unicdcdcdhd}(v5\_pre\_topc~\\
X2~X0~k3\_topmetr)))))\end{array}
\label{hyp:ehcdcdpfkghgchbgahigpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k3\_square\_1}~{X0}}={{{k3\_xcmplx\_0}~{X0}}~{X0}}})}}}\label{hyp:egbdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehgdpfkghgchbgahigpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)))))){\unicdbdjdcd}\\
(\preoh (v5\_pre\_topc~X1~X0~k3\_topmetr){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k3\_topmetr)))))){\unicdbdjdcd}(\preoh ({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}((k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)~X1~X3=X4){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k3\_topmetr)~X2~X3=k3\_square\_1~X4)))){\unicdcdcdhd}(v5\_pre\_topc~\\
X2~X0~k3\_topmetr)))))\end{array}$$
\end{theorem}
\end{document}
