\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{t38\_graph\_5 (TMb7VRv9KbwA4MrR1nfjscmLkgwiBSMhhW2)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_graph\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}(k7\_graph\_5~\\
X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  (v7\_graph\_1~X1~X0){\unicdcdcdhd}((v1\_graph\_4~\\
X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))))~({\uniddcgcg} X1 : \iota .  True)~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egbdbdpfhgchbgahigpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)){\unicdbdjdcd}(k6\_graph\_5~X0~X1=ReplSep~\\
(toset~({\uniddcgcg} X2 : \iota .  (v7\_graph\_1~X2~X0){\unicdcdcdhd}((v1\_graph\_4~X2~X0){\unicdcdcdhd}(m2\_graph\_1~\\
X2~X0))))~({\uniddcgcg} X2 : \iota .  (X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_funct\_1~(u1\_graph\_1~\\
X0)~(k1\_funct\_1~X2~np\_\_1)=k1\_funct\_1~(u1\_graph\_1~X0)~(k1\_funct\_1~\\
X1~np\_\_1)){\unicdcdcdhd}((k1\_funct\_1~(u2\_graph\_1~X0)~(k1\_funct\_1~X2~(k3\_finseq\_1~\\
X2))=k1\_funct\_1~(u2\_graph\_1~X0)~(k1\_funct\_1~X1~(k3\_finseq\_1~X1))){\unicdcdcdhd}\\
(r1\_tarski~(k10\_xtuple\_0~X2)~(k10\_xtuple\_0~X1)))))~({\uniddcgcg} X2 : \iota .  \\
X2)))\end{array}
\label{hyp:egbdadpfhgchbgahigpffd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfhgchbgahigpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)){\unicdbdjdcd}(r1\_tarski~(k6\_graph\_5~\\
X0~X1)~(k7\_graph\_5~X0)))\end{array}$$
\end{theorem}
\end{document}
