\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}
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\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\_graphsp (TMF5yx8xd6jStPghf7WBsTo8vbm1qjKumqs)}
\maketitle
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 $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_graphsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_graphsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_graphsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ r1\_graphsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k17\_graphsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_finseq\_2}~{({{k3\_finseq\_2}~{X0}})}}~{X0}}}\label{hyp:egehpflgddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(m2\_funct\_2~(k19\_graphsp~\\
X0)~(k3\_finseq\_2~k1\_numbers)~(k3\_finseq\_2~k1\_numbers)~(k9\_funct\_2~\\
(k3\_finseq\_2~k1\_numbers)~(k3\_finseq\_2~k1\_numbers)))\end{array}
\label{hyp:egehpflgbdjdpfhgchbgahigdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~(k3\_finseq\_2~k1\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}(m2\_finseq\_2~(k18\_graphsp~X0~X1)~\\
k1\_numbers~(k3\_finseq\_2~k1\_numbers))\end{array}
\label{hyp:egehpflgbdidpfhgchbgahigdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_funct\_2~X1~(k3\_finseq\_2~k1\_numbers)~(k3\_finseq\_2~k1\_numbers)~\\
(k9\_funct\_2~(k3\_finseq\_2~k1\_numbers)~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
((X1=k19\_graphsp~X0){\unicdbdjded}((k9\_xtuple\_0~X1=k3\_finseq\_2~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}\\
(k6\_graphsp~X1~X2=k18\_graphsp~X2~X0)))))\end{array}
\label{hyp:egbdfdpfhgchbgahigdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_2~X0~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_2~X2~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}((X2=k18\_graphsp~\\
X0~X1){\unicdbdjded}((k4\_finseq\_1~X2=k4\_finseq\_1~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X3 \in k4\_finseq\_1~X0){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X3~(k4\_nat\_1~np\_\_2~X1)){\unicdbdjdcd}((r1\_xxreal\_0~X3~X1){\unicdcdcdid}(((r1\_graphsp~X1~\\
(k7\_nat\_d~X3~X1)~X0){\unicdbdjdcd}(k1\_seq\_1~X2~X3=k7\_partfun1~k1\_numbers~X0~\\
(k2\_nat\_1~(k2\_nat\_1~(k4\_nat\_1~X1~X1)~(k4\_nat\_1~np\_\_3~X1))~np\_\_1))){\unicdcdcdhd}\\
((\preoh r1\_graphsp~X1~(k7\_nat\_d~X3~X1)~X0){\unicdbdjdcd}(k1\_seq\_1~X2~X3=k1\_seq\_1~\\
X0~X3))))){\unicdcdcdhd}(((r1\_xxreal\_0~X3~(k4\_nat\_1~np\_\_3~X1)){\unicdbdjdcd}((r1\_xxreal\_0~\\
X3~(k4\_nat\_1~np\_\_2~X1)){\unicdcdcdid}(((r1\_graphsp~X1~(k7\_nat\_d~X3~(k4\_nat\_1~\\
np\_\_2~X1))~X0){\unicdbdjdcd}(k1\_seq\_1~X2~X3=k17\_graphsp~X0~X1~(k7\_nat\_d~X3~(k4\_nat\_1~\\
np\_\_2~X1)))){\unicdcdcdhd}((\preoh r1\_graphsp~X1~(k7\_nat\_d~X3~(k4\_nat\_1~np\_\_2~X1))~\\
X0){\unicdbdjdcd}(k1\_seq\_1~X2~X3=k1\_seq\_1~X0~X3))))){\unicdcdcdhd}((\preoh (\preoh r1\_xxreal\_0~X3~X1){\unicdcdcdhd}\\
(r1\_xxreal\_0~X3~(k4\_nat\_1~np\_\_3~X1))){\unicdbdjdcd}(k1\_seq\_1~X2~X3=k1\_seq\_1~\\
X0~X3))))))))))\end{array}
\label{hyp:egbdedpfhgchbgahigdhah}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfhgchbgahigdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_2~X1~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}(k4\_finseq\_1~\\
(k6\_graphsp~(k19\_graphsp~X0)~X1)=k4\_finseq\_1~X1))\end{array}$$
\end{theorem}
\end{document}
