\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{t19\_jgraph\_6 (TMXiPVWBMXD6moEuRQK2ehGkPcj3LBXo1xq)}
\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_sppol\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\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 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}(k1\_sppol\_2~X0~X1~X2~X3=ReplSep~(toset~\\
({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~\\
({\uniddcgcg} X4 : \iota .  \preoh (\preoh (k17\_euclid~X4=X0){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_euclid~\\
X4)~X3){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k18\_euclid~X4)))){\unicdcdcdhd}((\preoh (r1\_xxreal\_0~(\\
k17\_euclid~X4)~X1){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k17\_euclid~X4)){\unicdcdcdhd}(k18\_euclid~\\
X4=X3))){\unicdcdcdhd}((\preoh (r1\_xxreal\_0~(k17\_euclid~X4)~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
X0~(k17\_euclid~X4)){\unicdcdcdhd}(k18\_euclid~X4=X2))){\unicdcdcdhd}(\preoh (k17\_euclid~X4=X1){\unicdcdcdhd}\\
((r1\_xxreal\_0~(k18\_euclid~X4)~X3){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k18\_euclid~\\
X4)))))))~({\uniddcgcg} X4 : \iota .  X4))))))\end{array}
\label{hyp:ehfdedpfdhahahpgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfkghgchbgahigpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(\\
(r1\_xxreal\_0~X2~X3){\unicdcdcdhd}(X4 \in k1\_sppol\_2~X0~X1~X2~X3))){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~(k17\_euclid~X4)){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~X4)~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
X2~(k18\_euclid~X4)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X4)~X3)))))))))\end{array}$$
\end{theorem}
\end{document}
