\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{t2\_jgraph\_6 (TMVmREspaD8ocJhcwYLwwqKrtV859mkDmxw)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ 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 $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((k17\_euclid~X0=k17\_euclid~X1){\unicdcdcdhd}((k17\_euclid~X1=k17\_euclid~\\
X2){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_euclid~X0)~(k18\_euclid~X1)){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k18\_euclid~X1)~(k18\_euclid~X2))))){\unicdbdjdcd}(X1 \in k1\_rltopsp1~(k15\_euclid~\\
np\_\_2)~X0~X2))))\end{array}
\label{hyp:ehhdpfhgpgcgpgbgcheghd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((k17\_euclid~\\
(k19\_euclid~X0~X1)=X0){\unicdcdcdhd}(k18\_euclid~(k19\_euclid~X0~X1)=X1)))\end{array}
\label{hyp:ehfdcdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k19\_euclid~X0~X1)~(u1\_struct\_0~(k15\_euclid~np\_\_2)))\end{array}
\label{hyp:egehpflgbdjdpffgfhdgmgjgeg}
\end{equation}
\begin{theorem}\label{thm:ehcdpfkghgchbgahigpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}(((k17\_euclid~X3=X0){\unicdcdcdhd}((r1\_xxreal\_0~X1~(k18\_euclid~\\
X3)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X3)~X2))){\unicdbdjdcd}((r1\_xxreal\_0~X2~X1){\unicdcdcdid}\\
(X3 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~X0~X1)~(k19\_euclid~\\
X0~X2)))))))\end{array}$$
\end{theorem}
\end{document}
