\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{t64\_jgraph\_6 (TMPWGczEMdx7DDhm7vU7TivXkQ6JshWrYj9)}
\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 $ r1\_jordan6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_sppol\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\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.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}((X4 \in k1\_rltopsp1~(k15\_euclid~\\
np\_\_2)~(k19\_euclid~X0~X2)~(k19\_euclid~X0~X3)){\unicdbdjdcd}((r1\_xxreal\_0~X1~\\
X0){\unicdcdcdid}((r1\_xxreal\_0~X3~X2){\unicdcdcdid}((r1\_jordan6~(k1\_sppol\_2~X0~X1~X2~X3)~\\
X4~X5){\unicdbdjded}(\preoh (\preoh (X5 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~X0~\\
X2)~(k19\_euclid~X0~X3)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X4)~(k18\_euclid~\\
X5))){\unicdcdcdhd}((\preoh X5 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~X0~X3)~\\
(k19\_euclid~X1~X3)){\unicdcdcdhd}((\preoh X5 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~\\
X1~X3)~(k19\_euclid~X1~X2)){\unicdcdcdhd}(\preoh (X5 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~\\
(k19\_euclid~X1~X2)~(k19\_euclid~X0~X2)){\unicdcdcdhd}(X5{\unicdcdgdad}k18\_pscomp\_1~(k1\_sppol\_2~\\
X0~X1~X2~X3)))))))))))))))\end{array}
\label{hyp:ehfdjdpfkghgchbgahigpfgd}
\end{equation}
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}((k18\_pscomp\_1~(k1\_sppol\_2~X0~X1~X2~\\
X3)=k19\_euclid~X0~X2){\unicdcdcdhd}(k22\_pscomp\_1~(k1\_sppol\_2~X0~X1~X2~X3)=k19\_euclid~\\
X1~X3))))))\end{array}
\label{hyp:ehedgdpfkghgchbgahigpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchngbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_1}}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchngbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{{k1\_real\_1}~{X0}}={{k4\_xcmplx\_0}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k1\_real\_1~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehgdedpfkghgchbgahigpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(\preoh (r1\_jordan6~(k1\_sppol\_2~(k1\_real\_1~np\_\_1)~np\_\_1~(k1\_real\_1~\\
np\_\_1)~np\_\_1)~X0~X1){\unicdcdcdhd}((X0 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~\\
(k1\_real\_1~np\_\_1)~(k1\_real\_1~np\_\_1))~(k19\_euclid~(k1\_real\_1~np\_\_1)~\\
np\_\_1)){\unicdcdcdhd}((\preoh (X1 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~(\\
k1\_real\_1~np\_\_1)~(k1\_real\_1~np\_\_1))~(k19\_euclid~(k1\_real\_1~np\_\_1)~\\
np\_\_1)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X0)~(k18\_euclid~X1))){\unicdcdcdhd}((\preoh X1 \in \\
k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~(k1\_real\_1~np\_\_1)~\\
np\_\_1)~(k19\_euclid~np\_\_1~np\_\_1)){\unicdcdcdhd}((\preoh X1 \in k1\_rltopsp1~(k15\_euclid~\\
np\_\_2)~(k19\_euclid~np\_\_1~np\_\_1)~(k19\_euclid~np\_\_1~(k1\_real\_1~np\_\_1))){\unicdcdcdhd}\\
(\preoh (X1 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~(k19\_euclid~np\_\_1~(k1\_real\_1~\\
np\_\_1))~(k19\_euclid~(k1\_real\_1~np\_\_1)~(k1\_real\_1~np\_\_1))){\unicdcdcdhd}(X1{\unicdcdgdad}\\
k19\_euclid~(k1\_real\_1~np\_\_1)~(k1\_real\_1~np\_\_1)))))))))\end{array}$$
\end{theorem}
\end{document}
