\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{t23\_jgraph\_7 (TMVAJV4Sf7y44M1oNaCancRyRzpzzGP1y5s)}
\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 $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_jordan17 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ r1\_jordan6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\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 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(((\\
r1\_xxreal\_0~(k18\_euclid~X1)~(k18\_euclid~X0)){\unicdcdcdhd}((r1\_xxreal\_0~(\\
k18\_euclid~X0)~X3){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~X1)~X2))){\unicdbdjdcd}((r1\_xxreal\_0~\\
X3~(k18\_euclid~X1)){\unicdcdcdid}((r1\_xxreal\_0~(k17\_euclid~X1)~(k17\_euclid~\\
X0)){\unicdcdcdid}(r1\_jordan6~(k1\_sppol\_2~(k17\_euclid~X0)~X2~(k18\_euclid~X1)~\\
X3)~X0~X1)))))))\end{array}
\label{hyp:ehgdpfkghgchbgahigpfhd}
\end{equation}
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 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v1\_xreal\_0~X4){\unicdbdjdcd}(((k17\_euclid~X0=k17\_euclid~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
X3~(k18\_euclid~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X1)~X4))){\unicdbdjdcd}((r1\_xxreal\_0~\\
X2~(k17\_euclid~X0)){\unicdcdcdid}((r1\_xxreal\_0~(k18\_euclid~X1)~(k18\_euclid~\\
X0)){\unicdcdcdid}(r1\_jordan6~(k1\_sppol\_2~(k17\_euclid~X0)~X2~X3~X4)~X0~X1))))))))\end{array}
\label{hyp:ehddpfkghgchbgahigpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X2)){\unicdbdjdcd}\\
(r1\_xxreal\_0~X0~X2))))\end{array}
\label{hyp:ehcdpfihihchfgbgmgpfad}
\end{equation}
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 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v1\_xreal\_0~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}(((k18\_euclid~X0=\\
X4){\unicdcdcdhd}((k18\_euclid~X1=X4){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~X0)~X3))){\unicdbdjdcd}\\
((r1\_xxreal\_0~X3~X2){\unicdcdcdid}((r1\_xxreal\_0~X5~X4){\unicdcdcdid}((r1\_xxreal\_0~(k17\_euclid~\\
X1)~X2){\unicdcdcdid}((r1\_xxreal\_0~(k17\_euclid~X0)~(k17\_euclid~X1)){\unicdcdcdid}(r1\_jordan6~\\
(k1\_sppol\_2~X2~X3~X4~X5)~X0~X1)))))))))))\end{array}
\label{hyp:ehbdcdpfkghgchbgahigpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}\\
((v1\_xreal\_0~X1){\unicdcdcdhd}((v1\_xreal\_0~X2){\unicdcdcdhd}(v1\_xreal\_0~X3)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_sppol\_2~X0~X1~X2~X3)~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))))\end{array}
\label{hyp:egehpflgbdpfdhahahpgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k18\_euclid~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k17\_euclid~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdhdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}((r1\_jordan17~X0~X1~X2~X3~X4){\unicdbdjded}(\preoh (\preoh (r1\_jordan6~X0~X1~X2){\unicdcdcdhd}\\
((r1\_jordan6~X0~X2~X3){\unicdcdcdhd}(r1\_jordan6~X0~X3~X4))){\unicdcdcdhd}((\preoh (r1\_jordan6~\\
X0~X2~X3){\unicdcdcdhd}((r1\_jordan6~X0~X3~X4){\unicdcdcdhd}(r1\_jordan6~X0~X4~X1))){\unicdcdcdhd}((\preoh (r1\_jordan6~\\
X0~X3~X4){\unicdcdcdhd}((r1\_jordan6~X0~X4~X1){\unicdcdcdhd}(r1\_jordan6~X0~X1~X2))){\unicdcdcdhd}(\preoh (r1\_jordan6~\\
X0~X4~X1){\unicdcdcdhd}((r1\_jordan6~X0~X1~X2){\unicdcdcdhd}(r1\_jordan6~X0~X2~X3)))))))))))\end{array}
\label{hyp:egbdpfkgpgchegbgogbdhd}
\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~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\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:ehcdddpfkghgchbgahigpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_xreal\_0~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(v1\_xreal\_0~X6){\unicdbdjdcd}({\unicdcdadad} X7 .  (v1\_xreal\_0~X7){\unicdbdjdcd}(((k17\_euclid~X0=\\
X4){\unicdcdcdhd}((k17\_euclid~X1=X4){\unicdcdcdhd}((k18\_euclid~X2=X6){\unicdcdcdhd}((k18\_euclid~X3=\\
X6){\unicdcdcdhd}((r1\_xxreal\_0~X6~(k18\_euclid~X0)){\unicdcdcdhd}((r1\_xxreal\_0~(k18\_euclid~\\
X1)~X7){\unicdcdcdhd}(r1\_xxreal\_0~(k17\_euclid~X2)~X5))))))){\unicdbdjdcd}((r1\_xxreal\_0~\\
X5~X4){\unicdcdcdid}((r1\_xxreal\_0~X7~X6){\unicdcdcdid}((r1\_xxreal\_0~(k18\_euclid~X1)~(k18\_euclid~\\
X0)){\unicdcdcdid}((r1\_xxreal\_0~(k17\_euclid~X3)~X4){\unicdcdcdid}((r1\_xxreal\_0~(k17\_euclid~\\
X2)~(k17\_euclid~X3)){\unicdcdcdid}(r1\_jordan17~(k1\_sppol\_2~X4~X5~X6~X7)~X0~X1~\\
X2~X3))))))))))))))\end{array}$$
\end{theorem}
\end{document}
