\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{t35\_jgraph\_6 (TMJ8RywzRvYsuQiagFPbsAMy4DHB67Dzvcs)}
\maketitle
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 $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfkghgchbgahigpfgd}
$$\begin{array}{c}ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))))~({\uniddcgcg} X0 : \iota .  \preoh (\preoh (k1\_real\_1~np\_\_1=k17\_euclid~X0){\unicdcdcdhd}(\\
(r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k18\_euclid~X0)~np\_\_1))){\unicdcdcdhd}((\preoh (k17\_euclid~X0=np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k1\_real\_1~np\_\_1)~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~\\
X0)~np\_\_1))){\unicdcdcdhd}((\preoh (k1\_real\_1~np\_\_1=k18\_euclid~X0){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k1\_real\_1~np\_\_1)~(k17\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~\\
X0)~np\_\_1))){\unicdcdcdhd}(\preoh (np\_\_1=k18\_euclid~X0){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_real\_1~\\
np\_\_1)~(k17\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~X0)~np\_\_1))))))~\\
({\uniddcgcg} X0 : \iota .  X0)=ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  \preoh (\preoh (k17\_euclid~\\
X0=k1\_real\_1~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~(k18\_euclid~\\
X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X0)~np\_\_1))){\unicdcdcdhd}((\preoh (k18\_euclid~X0=\\
np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~(k17\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k17\_euclid~X0)~np\_\_1))){\unicdcdcdhd}((\preoh (k17\_euclid~X0=np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k1\_real\_1~np\_\_1)~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~\\
X0)~np\_\_1))){\unicdcdcdhd}(\preoh (k18\_euclid~X0=k1\_real\_1~np\_\_1){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k1\_real\_1~np\_\_1)~(k17\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~\\
X0)~np\_\_1))))))~({\uniddcgcg} X0 : \iota .  X0)\end{array}$$
\end{theorem}
\end{document}
